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BEGIN:VEVENT
SUMMARY:Arnulf Jentzen (University of Münster)
DTSTART:20200824T130000Z
DTEND:20200824T140000Z
DTSTAMP:20260422T225756Z
UID:SNPDEA/1
DESCRIPTION:by Arnulf Jentzen (University of Münster) as part of "Partial
Differential Equations and Applications" Webinar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/SNPDEA/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julio D. Rossi (Universidad de Buenos Aires)
DTSTART:20200831T130000Z
DTEND:20200831T140000Z
DTSTAMP:20260422T225756Z
UID:SNPDEA/2
DESCRIPTION:Title: A
game theoretical approach for a nonlinear system driven by elliptic opera
tors\nby Julio D. Rossi (Universidad de Buenos Aires) as part of "Part
ial Differential Equations and Applications" Webinar\n\n\nAbstract\nThis t
alk is based on the interplay between partial differential equations and p
robability. \n\nWe find approximations using game theory to viscosity solu
tions to an elliptic system governed by two different operators (the Lapla
cian and the infinity Laplacian). \n\nWe analyze a game that combines Tug-
of-War with Random Walks in two different boards with a positive probabili
ty of jumping from one board to the other and we prove that the value func
tions for this game converge uniformly to a viscosity solution of an ellip
tic system as the step size goes to zero.\n\nIn addition\, we show uniquen
ess for the elliptic system using pure PDE techniques.\n\nJoint work with
A. Miranda (Buenos Aires).\n
LOCATION:https://researchseminars.org/talk/SNPDEA/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Bartsch (Universität Gießen)
DTSTART:20200907T130000Z
DTEND:20200907T140000Z
DTSTAMP:20260422T225756Z
UID:SNPDEA/3
DESCRIPTION:Title: N
ormalized solutions of nonlinear elliptic problems\nby Thomas Bartsch
(Universität Gießen) as part of "Partial Differential Equations and Appl
ications" Webinar\n\n\nAbstract\nThe talk will be concerned with the exist
ence of $L^2$ normalized solutions to nonlinear elliptic equations and sys
tems. A model problem is the system of nonlinear Schrödinger equations\n\
n$$-\\Delta u+\\lambda_1 u = \\mu_1 u^3 + \\beta u v^2 \\qquad \\in \\math
bb{R}^3$$\n$$-\\Delta v+\\lambda_2 v = \\mu_2 v^3 + \\beta u^2 v \\qquad \
\in \\mathbb{R}^3$$\n\nwith normalization constraints\n\n$$\\int_{\\mathbb
{R}^3} u^2 = a^2 \\quad \\text{and}\\quad \\int_{\\mathbb{R}^3} v^2 = b^2
\\\, .$$\n\nWhereas nonlinear elliptic equations and systems have been in
vestigated intensively since the 1960s\, in comparison surprisingly little
\nis known about solutions with prescribed $L^2$ norms. We discuss this\np
roblem and survey recent results.\nThe talk is based on joint work with Lo
uis Jeanjean\, Yanyan Liu\,\nZhaoli Liu\, Nicola Soave\, Xuexiu Zhong\, We
nming Zou.\n
LOCATION:https://researchseminars.org/talk/SNPDEA/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Weinan E (Princeton University)
DTSTART:20200914T130000Z
DTEND:20200914T140000Z
DTSTAMP:20260422T225756Z
UID:SNPDEA/4
DESCRIPTION:Title: P
DE problems that arise from machine learning\nby Weinan E (Princeton U
niversity) as part of "Partial Differential Equations and Applications" We
binar\n\n\nAbstract\nTwo kinds of PDE problems arise from machine learning
. The continuous formulation of machine learning naturally gives rise to s
ome very elegant and challenging PDE (more precisely partial differential
and integral equations) problems. It is likely that understanding these P
DE problems will become fundamental issues in the mathematical theory of m
achine learning.\nMachine learning-based algorithms for PDEs also lead to
new questions about these PDEs\, for example\, new kinds of a priori estim
ates that are suited for the machine learning model. I will discuss both k
inds of problems.\n
LOCATION:https://researchseminars.org/talk/SNPDEA/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claudio Muñoz (Universidad de Chile)
DTSTART:20200921T130000Z
DTEND:20200921T140000Z
DTSTAMP:20260422T225756Z
UID:SNPDEA/5
DESCRIPTION:Title: U
nderstanding soliton dynamics in Boussinesq models\nby Claudio Muñoz
(Universidad de Chile) as part of "Partial Differential Equations and Appl
ications" Webinar\n\n\nAbstract\nThe purpose of this talk is to describe i
n simple terms the soliton problem for several Boussinesq models\, includi
ng good\, improved and abcd systems. The problem is not simple\, because s
ome particular unstable behavior present in each system above mentioned. T
he idea is to explain the particularities of each system\, previous and re
cent results\, and future research\, in simple words.\n
LOCATION:https://researchseminars.org/talk/SNPDEA/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yihong Du (University of New England)
DTSTART:20200928T130000Z
DTEND:20200928T140000Z
DTSTAMP:20260422T225756Z
UID:SNPDEA/6
DESCRIPTION:Title: L
ong-time dynamics of the Fisher-KPP equation with nonlocal diffusion and f
ree boundary\nby Yihong Du (University of New England) as part of "Par
tial Differential Equations and Applications" Webinar\n\n\nAbstract\nWe co
nsider the Fisher-KPP equation with free boundary and "nonlocal diffusion"
. We show the problem is well-posed\, and its long-time dynamical behavior
is governed by a spreading-vanishing dichotomy. Moreover\, we completely
determine the spreading profile\, which may have a finite spreading speed
determined by a semi-wave problem\, or have infinite spreading speed (acce
lerated spreading)\, according to whether a threshold condition on the ker
nel function is satisfied. Further more\, for some typical kernel function
s\, we obtain sharp estimates of the spreading speed (whether finite or in
finite).\n
LOCATION:https://researchseminars.org/talk/SNPDEA/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:George Em Karniadakis (Brown University and MIT)
DTSTART:20201005T130000Z
DTEND:20201005T140000Z
DTSTAMP:20260422T225756Z
UID:SNPDEA/7
DESCRIPTION:Title: F
rom PINNs to DeepOnets: Approximating functions\, functionals\, and operat
ors using deep neural networks\nby George Em Karniadakis (Brown Univer
sity and MIT) as part of "Partial Differential Equations and Applications"
Webinar\n\n\nAbstract\nWe will present a new approach to develop a data-d
riven\, learning-based framework for predicting outcomes of physical and b
iological systems\, governed by PDEs\, and for discovering hidden physics
from noisy data. We will introduce a deep learning approach based on neura
l networks (NNs) and generative adversarial networks (GANs). We also intro
duce new NNs that learn functionals and nonlinear operators from functions
and corresponding responses for system identification. Unlike other appro
aches that rely on big data\, here we “learn” from small data by explo
iting the information provided by the physical conservation laws\, which a
re used to obtain informative priors or regularize the neural networks. We
will also make connections between Gauss Process Regression and NNs and d
iscuss the new powerful concept of meta-learning. We will demonstrate the
power of PINNs for several inverse problems in fluid mechanics\, solid mec
hanics and biomedicine including wake flows\, shock tube problems\, materi
al characterization\, brain aneurysms\, etc\, where traditional methods fa
il due to lack of boundary and initial conditions or material properties.\
n
LOCATION:https://researchseminars.org/talk/SNPDEA/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shi Jin (Shanghai Jiao Tong University)
DTSTART:20201012T130000Z
DTEND:20201012T140000Z
DTSTAMP:20260422T225756Z
UID:SNPDEA/8
DESCRIPTION:Title: R
andom Batch Methods for classical and quantum N-body problems\nby Shi
Jin (Shanghai Jiao Tong University) as part of "Partial Differential Equat
ions and Applications" Webinar\n\n\nAbstract\nWe first develop random batc
h methods for classical interacting particle systems with large number of
particles. These methods use small but random batches for particle intera
ctions\, thus the computational cost is reduced from O(N^2) per time step
to O(N)\, for a system with N particles with binary interactions. For one
of the methods\, we give a particle number independent error estimate unde
r some special interactions.\n\nThis method is also extended to quantum Mo
nte-Carlo methods for N-body Schrodinger equation and will be shown to hav
e significant gains in computational speed up over the classical Metropol
is-Hastings algorithm and the Langevin dynamics based Euler-Maruyama metho
d for statistical samplings of general distributions for interacting parti
cles. \n\nFor quantum N-body Schrodinger equation\, we also obtain\, for
pair-wise random interactions\, a convergence estimate for the Wigner tran
sform of the single-particle reduced density matrix of the particle system
at time t that is uniform in N > 1 and independent of the Planck constant
\\hbar. To this goal we need to introduce a new metric specially tailored
to handle at the same time the difficulties pertaining to the small \\hba
r regime (classical limit)\, and those pertaining to the large N regime (m
ean-field limit).\n\nThis talk is based on joint works with Lei Li\, Jian-
Guo Liu\, Francois Golse\, Thierry Paul and Xiantao Li.\n
LOCATION:https://researchseminars.org/talk/SNPDEA/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yoshikazu Giga (University of Tokyo)
DTSTART:20201019T130000Z
DTEND:20201019T140000Z
DTSTAMP:20260422T225756Z
UID:SNPDEA/9
DESCRIPTION:Title: O
n total variation flow type equations\nby Yoshikazu Giga (University o
f Tokyo) as part of "Partial Differential Equations and Applications" Webi
nar\n\n\nAbstract\nThe classical total variation flow is the $L^2$ gradien
t flow of the total variation. The total variation of a function u is one-
Dirichlet energy\, i.e.\,$ \\int |Du| dx$. Different from the Dirichlet en
ergy $\\int |Du|^2 dx/2$\, the energy density is singular at the place whe
re the slope of the function u equals zero. Because of this structure\, it
s gradient flow is actually non-local in the sense that the speed of slope
zero part (called a facet) is not determined by infinitesimal quantity. T
hus\, the definition of a solution itself is a nontrivial issue even for t
he classical total variation flow. This becomes more serious if there is n
on-uniform driving force term.\n\nRecently\, there need to study various t
ypes of such equations. A list of examples includes the total variation ma
p flow as well as the classical total variation flow and its fourth order
version in image de-noising\, crystalline mean curvature flow or fourth or
der total variation flow in crystal growth problems which are important mo
dels in materials science below roughening temperature.\n\nIn this talk\,
we survey recent progress on these equations with special emphasis on a cr
ystalline mean curvature flow whose solvability was left open more than te
n years. We shall give a global-in-time unique solvability in the level-se
t sense. It includes a recent extension when there is spatially non-unifor
m driving force term which is going to be published in the journal SN Part
ial Differential Equations. These last well-posedness results are based o
n my joint work with N. Požár (Kanazawa University) whose basic idea dep
ends on my earlier joint work with M.-H. Giga (The University of Tokyo) an
d N. Požár.\n
LOCATION:https://researchseminars.org/talk/SNPDEA/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jaeyoung Byeon (KAIST)
DTSTART:20201109T140000Z
DTEND:20201109T150000Z
DTSTAMP:20260422T225756Z
UID:SNPDEA/10
DESCRIPTION:Title:
Nonlinear Schrödinger systems with large interaction forces between diffe
rent components\nby Jaeyoung Byeon (KAIST) as part of "Partial Differe
ntial Equations and Applications" Webinar\n\n\nAbstract\nThere have been m
any studies on the asymptotic behavior of low energy solutions for a singl
e elliptic equation as an involved parameter approaches to a threshold. In
this case\, the asymptotic behavior depends on a balance between the diff
erential operator and nonlinearity\, and their interaction with a geometry
of a underlying domain. On the other hand\, even though the elliptic syst
ems coming from nonlinear Schrödinger systems have a simple looking inter
action terms\, even the construction of nontrivial low energy solutions is
not easy in general since the Morse indices of the nontrivial solutions c
ould be high depending types of interaction terms. \nWhen the interaction
forces between different components are very large\, we believe that a r
elatively simpler structure we can see. Nevertheless\, a wide variety of t
heir asymptotic behavior we could imagine as various kinds of combination
for the interaction between components might produce various effects on th
e asymptotic behavior. The general study for elliptic systems with large i
nteraction forces is quite challenging.\nIn this talk\, I would like to in
troduce my recent studies with collaborators on three components systemsas
basic steps to get general understanding for elliptic systems with large
interaction forces.\n
LOCATION:https://researchseminars.org/talk/SNPDEA/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Edriss Titi (University of Cambridge)
DTSTART:20201116T140000Z
DTEND:20201116T150000Z
DTSTAMP:20260422T225756Z
UID:SNPDEA/11
DESCRIPTION:Title:
The Inviscid Primitive Equations and the Effect of Rotation\nby Edriss
Titi (University of Cambridge) as part of "Partial Differential Equations
and Applications" Webinar\n\n\nAbstract\nLarge scale dynamics of the ocea
ns and the atmosphere is governed by the primitive equations (PEs). It is
well-known that the three-dimensional viscous primitive equations are glob
ally well-posed in Sobolev spaces. In this talk\, I will discuss the ill-p
osedness in Sobolev spaces\, the local well-posedness in the space of anal
ytic functions\, and the finite-time blowup of solutions to the three-dime
nsional inviscid PEs with rotation (Coriolis force). Eventually\, I will a
lso show\, in the case of ``well-prepared" analytic initial data\, the reg
ularizing effect of the Coriolis force by providing a lower bound for the
life-span of the solutions which grows toward infinity with the rotation r
ate. The latter is achieved by a delicate analysis of a simple limit reson
ant system whose solution approximate the corresponding solution of the 3D
inviscid PEs with the same initial data.\n
LOCATION:https://researchseminars.org/talk/SNPDEA/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierre-Emmanuel Jabin (University of Maryland)
DTSTART:20201123T140000Z
DTEND:20201123T150000Z
DTSTAMP:20260422T225756Z
UID:SNPDEA/12
DESCRIPTION:Title:
Large stochastic systems of interacting particles\nby Pierre-Emmanuel
Jabin (University of Maryland) as part of "Partial Differential Equations
and Applications" Webinar\n\n\nAbstract\nI will present some recent result
s\, obtained with D. Bresch and Z. Wang\, on large stochastic many-particl
e or multi-agent systems. Because such systems are conceptually simple but
exhibit a wide range of emerging macroscopic behaviors\, they are now emp
loyed in a large variety of applications from Physics (plasmas\, galaxy fo
rmation...) to the Biosciences\, Economy\, Social Sciences.\n\nThe number
of agents or particles is typically quite large\, with 1020-1025 particles
in many Physics settings for example and just as many equations. Analytic
al or numerical studies of such systems are potentially very complex lead
ing to the key question as to whether it is possible to reduce this comple
xity\, notably thanks to the notion of propagation of chaos (agents remain
ing almost uncorrelated). \n\nTo derive this propagation of chaos\, we hav
e introduced a novel analytical method\, which led to the resolution of tw
o long-standing conjectures: \n\n- The quantitative derivation of the 2-di
mensional incompressible Navier-Stokes system from the point vortices dyna
mics\; \n\n- The derivation of the mean-field limit for attractive singula
r interactions such as in the Keller-Segel model for chemotaxis and some C
oulomb gases.\n
LOCATION:https://researchseminars.org/talk/SNPDEA/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jose A. Carrillo (University of Oxford)
DTSTART:20201130T140000Z
DTEND:20201130T150000Z
DTSTAMP:20260422T225756Z
UID:SNPDEA/13
DESCRIPTION:Title:
Nonlinear Aggregation-Diffusion Equations: Gradient Flows\, Free Energies
and Phase Transitions\nby Jose A. Carrillo (University of Oxford) as p
art of "Partial Differential Equations and Applications" Webinar\n\n\nAbst
ract\nThe main goal of this talk is to discuss the state-of-the-art in und
erstanding the phenomena of phase transitions for a range of nonlinear Fok
ker-Planck equations with linear and nonlinear diffusion. They appear as n
atural macroscopic PDE descriptions of the collective behavior of particle
s such as Cucker-Smale models for consensus\, the Keller Segel model for c
hemotaxis\, and the Kuramoto model for synchronization. We will show the e
xistence of phase transitions in a variety of these models using the natur
al free energy of the system and their interpretation as natural gradient
flow structure with respect to the Wasserstein distance in probability mea
sures. We will discuss both theoretical aspects as well as numerical schem
es and simulations keeping those properties at the discrete level.\n
LOCATION:https://researchseminars.org/talk/SNPDEA/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marie E. Rognes (Simula)
DTSTART:20201207T140000Z
DTEND:20201207T150000Z
DTSTAMP:20260422T225756Z
UID:SNPDEA/14
DESCRIPTION:Title:
The brain's waterscape\nby Marie E. Rognes (Simula) as part of "Partia
l Differential Equations and Applications" Webinar\n\n\nAbstract\nYour bra
in has its own waterscape: whether you are reading or sleeping\, fluid flo
ws around or through the brain tissue and clears waste in the process. The
se physiological processes are crucial for the well-being of the brain. In
spite of their importance we understand them but little. Mathematics and
numerics could play a crucial role in gaining new insight. Indeed\, medica
l doctors express an urgent need for modeling of water transport through t
he brain\, to overcome limitations in traditional techniques. Surprisingly
little attention has been paid to the numerics of the brain’s waterscap
e however\, and fundamental knowledge is missing. In this talk\, I will di
scuss mathematical models and numerical methods for the brain's waterscape
across scales - from viewing the brain as a poroelastic medium at the mac
roscale and zooming in to studying electrical\, chemical and mechanical in
teractions between brain cells at the microscale.\n
LOCATION:https://researchseminars.org/talk/SNPDEA/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Susanna Terracini (Università di Torino)
DTSTART:20201026T140000Z
DTEND:20201026T150000Z
DTSTAMP:20260422T225756Z
UID:SNPDEA/15
DESCRIPTION:Title:
Segregation\, interaction of species and related free boundary problems\nby Susanna Terracini (Università di Torino) as part of "Partial Differ
ential Equations and Applications" Webinar\n\n\nAbstract\nReaction-diffusi
on systems with strong interaction terms appear in many multi-species phy
sical problems as well as in population dynamics\, chemistry and material
science. The qualitative properties of the solutions and their limiting pr
ofiles in different regimes have been at the center of the community's att
ention in recent years. A prototypical example appears when looking for so
litary wave solutions for Bose-Einstein condensates of two (or more) diffe
rent hyperfine states which overlap in space. Typically the forces between
particles in the same state are attractive while those between particles
in different states can be either attractive or repulsive. If the condensa
tes repel\, they eventually separate spatially giving rise to a free boun
dary. This phenomenon is called phase separation and has been described in
recent literature\, both physical and mathematical. \n\nOne of the most
interesting problems researchers investigate is when different phases of m
atter\, populations\, or clusters exist in a single space (i.e. in adjacen
t cells). Their interest focuses not only in how these different phases/p
opulations/clusters interact with one another\, but also on the properties
of the boundaries separating them. The recent literature shows that the w
alls separating the different phases are geometrically tractable surfaces\
, as well as multiple junctions among them. This involves developing novel
variational methods and geometric measure theory and free boundary tools.
Relevant connections have been established with optimal partition proble
ms involving spectral functionals. The classification of entire solutions
and the geometric aspects of the nodal sets of solutions are of fundament
al importance as well. We intend to focus on the most recent development o
f the theory in connection with problems featuring anomalous diffusions\,
long-range and non symmetric.\n
LOCATION:https://researchseminars.org/talk/SNPDEA/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yanyan Li (Rutgers)
DTSTART:20201102T140000Z
DTEND:20201102T150000Z
DTSTAMP:20260422T225756Z
UID:SNPDEA/16
DESCRIPTION:Title:
Gradient estimates for the insulated conductivity problem\nby Yanyan L
i (Rutgers) as part of "Partial Differential Equations and Applications" W
ebinar\n\n\nAbstract\nIn this talk\, we discuss the insulated conductivity
problem with multiple inclusions embedded in a bounded domain in n-dimens
ional Euclidean space. The gradient of a solution may blow up as two inclu
sions approach each other. The optimal blow up rate was known in dimension
n=2. It was not known whether the established upper bound of the blow up
rates in higher dimensions were optimal.\nWe answer this question by impro
ving the previously known upper bound of the blow up rates in dimension n>
2.\nThis is a joint work with Zhuolun Yang.\n
LOCATION:https://researchseminars.org/talk/SNPDEA/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marie-Therese Wolfram (University of Warwick)
DTSTART:20201214T140000Z
DTEND:20201214T150000Z
DTSTAMP:20260422T225756Z
UID:SNPDEA/17
DESCRIPTION:Title:
On mean-field models in pedestrian dynamics\nby Marie-Therese Wolfram
(University of Warwick) as part of "Partial Differential Equations and App
lications" Webinar\n\n\nAbstract\nIn this talk I will start with a general
overview on mean-field models for pedestrian dynamics\, outlining the cha
llenges in the derivation and the analysis of the corresponding PDE models
. I will then illustrate how this continuum description can be used to und
erstand the effect of inflow and outflow rates as well as the geometry on
pedestrian density profiles. Finally I will present how the Bayesian fram
ework can be used to identify parameters in mean field models and quantify
uncertainty in those estimates using trajectory data.\n
LOCATION:https://researchseminars.org/talk/SNPDEA/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Huyên Pham (Paris Diderot)
DTSTART:20210208T140000Z
DTEND:20210208T150000Z
DTSTAMP:20260422T225756Z
UID:SNPDEA/18
DESCRIPTION:by Huyên Pham (Paris Diderot) as part of "Partial Differentia
l Equations and Applications" Webinar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/SNPDEA/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eitan Tadmor (University of Maryland)
DTSTART:20210215T140000Z
DTEND:20210215T150000Z
DTSTAMP:20260422T225756Z
UID:SNPDEA/19
DESCRIPTION:by Eitan Tadmor (University of Maryland) as part of "Partial D
ifferential Equations and Applications" Webinar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/SNPDEA/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Diogo Gomes (KAUST)
DTSTART:20210222T140000Z
DTEND:20210222T150000Z
DTSTAMP:20260422T225756Z
UID:SNPDEA/20
DESCRIPTION:by Diogo Gomes (KAUST) as part of "Partial Differential Equati
ons and Applications" Webinar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/SNPDEA/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Markus Melenk (TU Wien)
DTSTART:20210304T140000Z
DTEND:20210304T150000Z
DTSTAMP:20260422T225756Z
UID:SNPDEA/21
DESCRIPTION:Title:
High order numerical methods for fractional diffusion in polygons\nby
Markus Melenk (TU Wien) as part of "Partial Differential Equations and App
lications" Webinar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/SNPDEA/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kanishka Perera (Florida Tech)
DTSTART:20210311T140000Z
DTEND:20210311T150000Z
DTSTAMP:20260422T225756Z
UID:SNPDEA/22
DESCRIPTION:Title:
An abstract critical point theorem with applications to elliptic problems
with combined nonlinearities\nby Kanishka Perera (Florida Tech) as par
t of "Partial Differential Equations and Applications" Webinar\n\nAbstract
: TBA\n
LOCATION:https://researchseminars.org/talk/SNPDEA/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giuseppe Mingione (Università di Parma)
DTSTART:20210318T140000Z
DTEND:20210318T150000Z
DTSTAMP:20260422T225756Z
UID:SNPDEA/23
DESCRIPTION:Title:
Nonuniformly elliptic problems\nby Giuseppe Mingione (Università di P
arma) as part of "Partial Differential Equations and Applications" Webinar
\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/SNPDEA/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mouhamed Moustapha Fall (AIMS-Senegal)
DTSTART:20210325T140000Z
DTEND:20210325T150000Z
DTSTAMP:20260422T225756Z
UID:SNPDEA/24
DESCRIPTION:Title:
Constant (nonlocal) Mean curvature surfaces\nby Mouhamed Moustapha Fal
l (AIMS-Senegal) as part of "Partial Differential Equations and Applicatio
ns" Webinar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/SNPDEA/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Camillo De Lellis (IAS Princeton)
DTSTART:20210429T130000Z
DTEND:20210429T140000Z
DTSTAMP:20260422T225756Z
UID:SNPDEA/25
DESCRIPTION:Title:
Flows of vector fields: classical and modern\nby Camillo De Lellis (IA
S Princeton) as part of "Partial Differential Equations and Applications"
Webinar\n\n\nAbstract\nConsider a (possibly time-dependent) vector field $
v$ on the Euclidean space. The classical Cauchy-Lipschitz (also named Pica
rd-Lindelöf) Theorem states that\, if the vector field $v$ is Lipschitz i
n space\, for every initial datum $x$ there is a unique trajectory $\\gamm
a$ starting at $x$ at time $0$ and solving the ODE $\\dot{\\gamma} (t) = v
(t\, \\gamma (t))$. The theorem looses its validity as soon as $v$ is sli
ghtly less regular. However\, if we bundle all trajectories into a global
map allowing $x$ to vary\, a celebrated theory put forward by DiPerna and
Lions in the 80es show that there is a unique such flow under very reasona
ble conditions and for much less regular vector fields. A long-standing op
en question is whether this theory is the byproduct of a stronger classica
l result which ensures the uniqueness of trajectories for almost every ini
tial datum. I will give a complete answer to the latter question and draw
connections with partial differential equations\, harmonic analysis\, prob
ability theory and Gromov's $h$-principle.\n
LOCATION:https://researchseminars.org/talk/SNPDEA/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ian Tice (CMU)
DTSTART:20210506T130000Z
DTEND:20210506T140000Z
DTSTAMP:20260422T225756Z
UID:SNPDEA/26
DESCRIPTION:Title:
Traveling wave solutions to the free boundary Navier-Stokes equations\
nby Ian Tice (CMU) as part of "Partial Differential Equations and Applicat
ions" Webinar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/SNPDEA/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christian Kühn (TU Munich)
DTSTART:20210513T130000Z
DTEND:20210513T140000Z
DTSTAMP:20260422T225756Z
UID:SNPDEA/27
DESCRIPTION:Title:
Geometric Singular Perturbation Theory for Fast-Slow PDEs\nby Christia
n Kühn (TU Munich) as part of "Partial Differential Equations and Applica
tions" Webinar\n\n\nAbstract\nSystems with multiple time scales appear in
a wide variety of applications. Yet\, their mathematical analysis is chall
enging already in the context of ODEs\, where about four decades were need
ed to develop a more comprehensive theory based upon invariant manifolds\,
desingularization\, variational equations\, and many other techniques.\nY
et\, for PDEs progress has been extremely slow due to many obstacles in ge
neralizing several ODE methods. In my talk\, I shall report on two recent
advances for fast-slow PDEs\, namely the extension of slow manifold theory
for unbounded operators driving the slow variables\, and the design of a
blow-up method for PDEs\, where normal hyperbolicity is lost. This is join
t work with Maximilian Engel and Felix Hummel.\n
LOCATION:https://researchseminars.org/talk/SNPDEA/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hung Vinh Tran (University of Wisconsin Madison)
DTSTART:20210520T130000Z
DTEND:20210520T140000Z
DTSTAMP:20260422T225756Z
UID:SNPDEA/28
DESCRIPTION:Title:
Large time behavior and large time profile of viscous Hamilton-Jacobi equa
tions\nby Hung Vinh Tran (University of Wisconsin Madison) as part of
"Partial Differential Equations and Applications" Webinar\n\n\nAbstract\nI
will describe our recent results on large time behavior and large time pr
ofile of viscous Hamilton-Jacobi equations in the periodic setting. Here\,
the diffusion matrix might be degenerate\, which makes the problem more d
ifficult and challenging. Based on joint works with Cagnetti\, Gomes\, Mit
ake.\n
LOCATION:https://researchseminars.org/talk/SNPDEA/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chi-Wang Shu (Brown University)
DTSTART:20210527T130000Z
DTEND:20210527T140000Z
DTSTAMP:20260422T225756Z
UID:SNPDEA/29
DESCRIPTION:Title:
Stability of time discretizations for semi-discrete high order schemes for
time-dependent PDEs\nby Chi-Wang Shu (Brown University) as part of "P
artial Differential Equations and Applications" Webinar\n\n\nAbstract\nIn
scientific and engineering computing\, we encounter time-dependent partial
differential equations (PDEs) frequently. When designing high order sche
mes for solving these time-dependent PDEs\, we often first develop semi-di
screte schemes paying attention only to spatial discretizations and leavin
g time $t$ continuous. It is then important to have a high order time dis
cretization to main the stability properties of the semi-discrete schemes.
In this talk we discuss several classes of high order time discretizatio
n\, including the strong stability preserving (SSP) time discretization\,
which preserves strong stability from a stable spatial discretization with
Euler forward\, the implicit-explicit (IMEX) Runge-Kutta or multi-step ti
me marching\, which treats the more stiff term (e.g. diffusion term in a c
onvection-diffusion equation) implicitly and the less stiff term (e.g. the
convection term in such an equation) explicitly\, for which strong stabil
ity can be proved under the condition that the time step is upper-bounded
by a constant under suitable conditions\, and the explicit Runge-Kutta met
hods\, for which strong stability can be proved in many cases for semi-neg
ative linear semi-discrete schemes. Numerical examples will be given to d
emonstrate the performance of these schemes.\n
LOCATION:https://researchseminars.org/talk/SNPDEA/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Mazzucato (Penn State)
DTSTART:20210603T130000Z
DTEND:20210603T140000Z
DTSTAMP:20260422T225756Z
UID:SNPDEA/30
DESCRIPTION:Title:
Direct and inverse problems for a model of dislocations in geophysics\
nby Anna Mazzucato (Penn State) as part of "Partial Differential Equations
and Applications" Webinar\n\n\nAbstract\nI will discuss a model for dislo
cations in an elastic medium\, modeling faults in the Earth's crust. The d
irect problem consists in solving a non-standard boundary value/interface
problem for isotropic\, in-homogeneous linear elasticity with piecewise Li
pschitz Lame' parameters\, for which we prove well-posedness and a double-
layer potential representation for the solution if the coefficients jumps
only along the fault. The non-linear inverse problem consists in determini
ng the fault surface and slip vector from displacement measurements made a
t the surface. We prove uniqueness under some geometric conditions\, using
unique continuation results for systems.\nWe also establish shape deriva
tive formulas under infinitesimal movements of the fault and changes in th
e slip. The application of the inverse problem is in fault monitoring and
microseismicity. This is joint work with Andrea Aspri (Pavia University)\
, Elena Beretta (Politechnico\, Milan & NYU-Abu Dhabi)\, and Maarten de Ho
op (Rice).\n
LOCATION:https://researchseminars.org/talk/SNPDEA/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Philipp Grohs (University of Vienna)
DTSTART:20210610T130000Z
DTEND:20210610T140000Z
DTSTAMP:20260422T225756Z
UID:SNPDEA/31
DESCRIPTION:Title:
Deep Learning in Numerical Analysis\nby Philipp Grohs (University of V
ienna) as part of "Partial Differential Equations and Applications" Webina
r\n\n\nAbstract\nThe development of new classification and regression algo
rithms based on deep neural networks coined Deep Learning have had a drama
tic impact in the areas of artificial intelligence\, machine learning\, an
d data analysis. More recently\, these methods have been applied successfu
lly to the numerical solution of partial differential equations (PDEs). Ho
wever\, a rigorous analysis of their potential and limitations is still la
rgely open. In this talk we will survey recent results contributing to suc
h an analysis. In particular I will present recent empirical and theoretic
al results supporting the capability of Deep Learning based methods to bre
ak the curse of dimensionality for several high dimensional PDEs\, includi
ng nonlinear Black Scholes equations used in computational finance\, Hamil
ton Jacobi Bellman equations used in optimal control\, and stationary Schr
ödinger equations used in quantum chemistry. Despite these encouraging re
sults\, it is still largely unclear for which problem classes a Deep Learn
ing based ansatz can be beneficial. To this end I will\, in a second part\
, present recent work establishing fundamental limitations on the computat
ional efficiency of Deep Learning based numerical algorithms that\, in par
ticular\, confirm a previously empirically observed "theory-to-practice ga
p".\n
LOCATION:https://researchseminars.org/talk/SNPDEA/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Apala Majumdar (University of Strathclyde)
DTSTART:20210617T130000Z
DTEND:20210617T140000Z
DTSTAMP:20260422T225756Z
UID:SNPDEA/32
DESCRIPTION:Title:
PDE problems in the Landau-de Gennes theory for Nematic Liquid Crystals\nby Apala Majumdar (University of Strathclyde) as part of "Partial Diffe
rential Equations and Applications" Webinar\n\n\nAbstract\nNematic liquid
crystals are classical examples of partially ordered materials that combin
e fluidity with the order of crystalline solids. Nematics have long-range
orientational order i.e. they are directional materials with special direc
tions\, referred to as directors. The Landau-de Gennes theory is one of th
e most celebrated and powerful continuum theories for nematic liquid cryst
als. In this talk\, we review the mathematical framework for the Landau-de
Gennes theory with emphasis on the Landau-de Gennes free energy and the a
ssociated Euler-Lagrange equations\, which are typically a system of coupl
ed\, nonlinear partial differential equations. We review some recent resul
ts for boundary-value problems in the Landau-de Gennes theory\, including
results on the multiplicity\, defect sets and asymptotic analysis of energ
y-minimizing solutions. We also describe the physical relevance of these s
olutions\, followed by case studies of applications in the physical scienc
es and industry.\n
LOCATION:https://researchseminars.org/talk/SNPDEA/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yoichiro Mori (University of Pennsylvania)
DTSTART:20210624T130000Z
DTEND:20210624T140000Z
DTSTAMP:20260422T225756Z
UID:SNPDEA/33
DESCRIPTION:Title:
Analysis of the Dynamics of Immersed Elastic Filaments in Stokes Flow\
nby Yoichiro Mori (University of Pennsylvania) as part of "Partial Differe
ntial Equations and Applications" Webinar\n\n\nAbstract\nWe consider the p
roblem of an elastic filament immersed in a 2D or 3D Stokes fluid. We firs
t discuss the analysis of an immersed filament problem in a 2D Stokes flui
d (the Peskin problem). We prove well-posedness and immediate regularizati
on of the elastic filament configuration and discuss criteria for global e
xistence. We will then discuss the immersed filament problem in a 3D Stoke
s fluid (the Slender Body problem). Here\, it has not even been clear what
the appropriate mathematical formulation of the problem should be. We pro
pose a mathematical formulation for the Slender Body problem and discuss w
ell-posedness for the stationary version of this problem. Furthermore\, we
prove that the Slender Body approximation\, introduced by Keller and Rubi
now in the 1980's and used widely in computation\, provides an approximati
on to the Slender Body problem.\n
LOCATION:https://researchseminars.org/talk/SNPDEA/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Enrico Valdinoci (University of Western Australia)
DTSTART:20210923T130000Z
DTEND:20210923T140000Z
DTSTAMP:20260422T225756Z
UID:SNPDEA/34
DESCRIPTION:Title:
Nonlocal minimal surfaces are generically sticky\nby Enrico Valdinoci
(University of Western Australia) as part of "Partial Differential Equatio
ns and Applications" Webinar\n\n\nAbstract\nSurfaces which minimize a nonl
ocal perimeter functional exhibit quite different behaviors than the ones
minimizing the classical perimeter. Among these peculiar features\, an int
eresting property\, which is also in contrast with the pattern produced by
the solutions of linear equations\, is given by the capacity\, and the st
rong tendency\, of adhering at the boundary. We will discuss this phenomen
on and present some recent results.\n
LOCATION:https://researchseminars.org/talk/SNPDEA/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fernando Quirós (Universidad Autónoma de Madrid)
DTSTART:20210930T130000Z
DTEND:20210930T140000Z
DTSTAMP:20260422T225756Z
UID:SNPDEA/35
DESCRIPTION:Title:
Travelling-wave behaviour in problems with degenerate diffusion\nby Fe
rnando Quirós (Universidad Autónoma de Madrid) as part of "Partial Diffe
rential Equations and Applications" Webinar\n\n\nAbstract\nWe review some
recent results on the large-time behaviour of solutions to certain reactio
n-diffusion equations involving a diffusion operator that degenerates at t
he level 0. Nonnegative solutions with compactly supported initial data ha
ve a compact support for any later time\, so that the problem has a free b
oundary whose asymptotic location one would like to determine.\n\nProblems
in this family have a unique (up to translations) travelling wave solutio
n with a finite front. When the initial datum is bounded\, radially symmet
ric and compactly supported\, we prove that solutions converging to 1 (whi
ch exist for all the reaction terms under consideration) do so by approach
ing a translation of this unique traveling wave in the radial direction\,
but with a logarithmic correction in the position of the front when the di
mension is bigger than one. As a corollary we obtain the asymptotic locati
on of the free boundary and level sets in the non-radial case up to an err
or term of size $O(1)$. A main technical tool of independent interest is a
n estimate for the flux.\n\nThis is a collaboration with Y. Du\, A. Gárri
z and M. Zhou.\n
LOCATION:https://researchseminars.org/talk/SNPDEA/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alessio Figalli (ETH Zürich)
DTSTART:20211021T130000Z
DTEND:20211021T140000Z
DTSTAMP:20260422T225756Z
UID:SNPDEA/36
DESCRIPTION:Title:
Free boundary regularity in the Stefan problem\nby Alessio Figalli (ET
H Zürich) as part of "Partial Differential Equations and Applications" We
binar\n\n\nAbstract\nThe Stefan problem describes phase transitions such a
s ice melting to water\, and it is among the most classical free boundary
problems. It is well known that the free boundary consists of a smooth par
t (the regular part) and singular points. In this talk\, I will describe a
recent result with Ros-Oton and Serra\, where we analyze the singular set
in the Stefan problem and prove a series of fine results on its structure
.\n
LOCATION:https://researchseminars.org/talk/SNPDEA/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Helena Nussenzveig Lopes (Universidade Federal do Rio de Janeiro)
DTSTART:20211028T130000Z
DTEND:20211028T140000Z
DTSTAMP:20260422T225756Z
UID:SNPDEA/37
DESCRIPTION:Title:
2D Navier-Stokes equations on a bounded domain with holes and Navier frict
ion boundary conditions\nby Helena Nussenzveig Lopes (Universidade Fed
eral do Rio de Janeiro) as part of "Partial Differential Equations and App
lications" Webinar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/SNPDEA/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Max Engelstein (University of Minnesota)
DTSTART:20211104T140000Z
DTEND:20211104T150000Z
DTSTAMP:20260422T225756Z
UID:SNPDEA/38
DESCRIPTION:Title:
Generic Smoothness for the nodal sets of solutions to the Dirichlet proble
m for Elliptic PDE\nby Max Engelstein (University of Minnesota) as par
t of "Partial Differential Equations and Applications" Webinar\n\nAbstract
: TBA\n
LOCATION:https://researchseminars.org/talk/SNPDEA/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniela De Silva
DTSTART:20211111T140000Z
DTEND:20211111T150000Z
DTSTAMP:20260422T225756Z
UID:SNPDEA/39
DESCRIPTION:Title:
Global minimizers to the one-phase free boundary problem\nby Daniela D
e Silva as part of "Partial Differential Equations and Applications" Webin
ar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/SNPDEA/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Henrik Shahgholian (Royal Institute of Technology)
DTSTART:20211118T140000Z
DTEND:20211118T150000Z
DTSTAMP:20260422T225756Z
UID:SNPDEA/40
DESCRIPTION:Title:
A free boundary perspective on transmission and inverse scattering problem
s\nby Henrik Shahgholian (Royal Institute of Technology) as part of "P
artial Differential Equations and Applications" Webinar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/SNPDEA/40/
END:VEVENT
END:VCALENDAR