BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Eduardo Cerpa (Pontificia Universidad Catolica de Chile\, Chile) DTSTART:20200922T110000Z DTEND:20200922T120000Z DTSTAMP:20260422T212705Z UID:WOPARA/1 DESCRIPTION:Title: C ontrol properties of a parabolic-elliptic system\nby Eduardo Cerpa (Po ntificia Universidad Catolica de Chile\, Chile) as part of Webinar on PDE and related areas\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/WOPARA/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Emil Wiedemann (Ulm university\, Germany) DTSTART:20200924T093000Z DTEND:20200924T103000Z DTSTAMP:20260422T212705Z UID:WOPARA/2 DESCRIPTION:Title: W eak and measure-valued solutions of the compressible Euler equations.\ nby Emil Wiedemann (Ulm university\, Germany) as part of Webinar on PDE an d related areas\n\n\nAbstract\nSeveral notions of weak or “very weak” solutions have been sug-gested for the incompressible and compressibl e Euler systems\, motivated bythe lack of a satisfactory well-posednes s theory for these equations in turbulentregimes. Surprisingly\, the spea ker and L. Sz ́ekelyhidi showed in 2012 that dis-tributional and measure- valued solutions are in a sense the same\, although thelatter had been expected to be a much weaker notion. In this talk\, we turnto the isentropic compressible Euler system\, where the situation is fundamen -tally different. Joint work with E. Chiodaroli\, E. Feireisl\, O. Kreml\, and D.Gallenmuller.\n LOCATION:https://researchseminars.org/talk/WOPARA/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Saugata Bandyopadhyay (IISER-Kolkata\, India) DTSTART:20200929T093000Z DTEND:20200929T103000Z DTSTAMP:20260422T212705Z UID:WOPARA/3 DESCRIPTION:Title: O n the Equation (∇u)^tH(u)(∇u) = G\nby Saugata Bandyopadhyay (IISER -Kolkata\, India) as part of Webinar on PDE and related areas\n\n\nAbstrac t\nLet n∈N\,n>2 and let Ω⊆R^n be open. Let H\, G:R^n→R^{n×n} be of appropriate regularity. We discuss the existence of an immersionu: Ω →R^n of appropriate regularity\, satisfying (∇u)^tH(u)(∇u) =G in Ω ......(1)\n\nWe consider Cauchy\, Dirichlet and Dirichlet-Neumann problems .Equation (1) comes up in diverse contexts. WhenH(and henceG) issymmetric and positive definite\, Equation (1) is connected to the prob-lem of equi valence of Riemannian metrics. The symmetric case is alsoimportant in the non-linear elasticity theory because of its connectionwith the Cauchy-Gre en deformation tensor. WhenH(and henceG) isskew-symmetric\, Equation (1) comes up in the context of the problemof equivalence of differential two-f orms.The aim of the talk is to present a survey of recent progress and ad- vances made in the context of Equation (1). We shall also discuss thegene ral case whenH\,Gare neither symmetric nor skew-symmetric.\n LOCATION:https://researchseminars.org/talk/WOPARA/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Siddhartha Mishra (ETH Zurich\, Switzerland) DTSTART:20201001T093000Z DTEND:20201001T103000Z DTSTAMP:20260422T212705Z UID:WOPARA/4 DESCRIPTION:Title: D eep Learning and Computations of PDEs\nby Siddhartha Mishra (ETH Zuric h\, Switzerland) as part of Webinar on PDE and related areas\n\n\nAbstract \nDeep neural networks are rapidly emerging as a key tool in en-hancing c omputations of PDEs. In this talk\, we survey recent development sin my research group on two related themes. First\, we use supervised le arningto approximate observables for PDEs efficiently with applications to UQ andPDE constrained optimization. Second\, we discuss recently introdu ced physicsinformed neural networks (PINNs) as an efficient discret ization tool for bothforward as well as inverse problems for certain cl asses of PDEs.\n LOCATION:https://researchseminars.org/talk/WOPARA/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Jean-Pierre Raymond (Institut de Mathématiques\, Université Paul Sabatier\, France) DTSTART:20201006T093000Z DTEND:20201006T103000Z DTSTAMP:20260422T212705Z UID:WOPARA/5 DESCRIPTION:Title: E xistence and uniqueness of maximal strong solution of a 1D Blood flow in a network of vessels\nby Jean-Pierre Raymond (Institut de Mathématique s\, Université Paul Sabatier\, France) as part of Webinar on PDE and rela ted areas\n\n\nAbstract\nn this talk\, we shall review some models used to describe bloodflows in the human brain. We shall give new existence\, un iqueness and stabilityresults for some of those models\, corresponding to systems of one-dimensionalpartial differential equations. We shall a lso prove a stability estimate undersuitable nonlinear Dirichlet boun dary conditions.Joint work with D. Maity and A. Roy.\n LOCATION:https://researchseminars.org/talk/WOPARA/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Jean-Michel Coron (Jacques-Louis Lions Laboratory\, Université Pi erre et Marie Curie\, France) DTSTART:20201008T093000Z DTEND:20201008T103000Z DTSTAMP:20260422T212705Z UID:WOPARA/6 DESCRIPTION:Title: S tabilization in finite time of some partial differential equations\nby Jean-Michel Coron (Jacques-Louis Lions Laboratory\, Université Pierre et Marie Curie\, France) as part of Webinar on PDE and related areas\n\n\nAb stract\nIn this talk we present some recent results on the stabilization i nfinite time of 1-D classical partial differential equations (as parabolic equations\,hyperbolic systems\, Korteweg-de Vries equations and the visco us Burgers equa-tion). We give some ideas of the proofs and present open problems.\n LOCATION:https://researchseminars.org/talk/WOPARA/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Gunther Uhlmann (University of Washington\, USA) DTSTART:20201013T123000Z DTEND:20201013T133000Z DTSTAMP:20260422T212705Z UID:WOPARA/7 DESCRIPTION:Title: S eeing Through Space Time\nby Gunther Uhlmann (University of Washington \, USA) as part of Webinar on PDE and related areas\n\n\nAbstract\ne consi der inverse problems for the Einstein equation with a time-depending metri c on a 4-dimensional globally hyperbolic Lorentzian manifold.We formulate the concept of active measurements for relativistic models. Wedo this by coupling Einstein equations with equations for scalar fields.The inverse p roblem we study is the question of whether the observationsof the solution s of the coupled system in an open subset of the space-time withthe source s supported in this set determines the metric in a larger domain. Tostudy this problem we define the concept of light observation sets a nd showthat knowledge of these sets determine the conformal class of the metric. Thiscorresponds to passive observations from a distant area of sp ace which is filledby light sources.We will start by considering inverse p roblems for scalar non-linear hyperbolicequations to explain our method. N o previous knowledge of Lorentzian geometryor general relativity will be a ssumed.This is based on joint work with P. Hinz\, Y. Kurylev\, M. Lassas\, Y. Wangand J. Zhai\n LOCATION:https://researchseminars.org/talk/WOPARA/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Eduard Feireisl (Institute of Mathematics AS CR\, Czech Republic) DTSTART:20201015T093000Z DTEND:20201015T103000Z DTSTAMP:20260422T212705Z UID:WOPARA/8 DESCRIPTION:Title: ( S)-convergence and approximation of oscillatory solutions in fluid dynamic s\nby Eduard Feireisl (Institute of Mathematics AS CR\, Czech Republic ) as part of Webinar on PDE and related areas\n\n\nAbstract\nWe propose a new concept of (S)-convergence applicable to nu-merical methods as well as other consistent approximations of the Euler systemin gas dynamics. (S)- convergence\, based on averaging in the spirit of StrongLaw of Large Numb ers\, reflects the asymptotic properties of a given approximatesequence be tter than the standard description via Young measures. Similaritywith the tools of ergodic theory is discussed\n LOCATION:https://researchseminars.org/talk/WOPARA/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Helge Holden (Norwegian University of Science and Technology\, Nor way) DTSTART:20201020T093000Z DTEND:20201020T103000Z DTSTAMP:20260422T212705Z UID:WOPARA/9 DESCRIPTION:Title: A Lipschitz metric for the Camassa–Holm equation\nby Helge Holden (No rwegian University of Science and Technology\, Norway) as part of Webinar on PDE and related areas\n\n\nAbstract\nThe Camassa—Holm equation u_t+uu _x+p_x= 0\, p−p_{xx}=u^2+1/2u_x^2 has received considerable attention since it was first studied by Camassa andHolm in 1993. Part of the intere st stems from the fact that the solution developssingularities in finite t ime while keeping theH1norm finite. At wave breakinguniqueness is lost as the there are infinitely many ways to extend the solutionbeyond wave brea king. We study the so-called conservative solutions and showhow to constr uct a Lipschitz metric comparing two conservative solutions.This is joint work with J. A. Carrillo (Imperial) and K. Grunert (NTNU).\n LOCATION:https://researchseminars.org/talk/WOPARA/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Laurent Véron (Universite de tour\, France) DTSTART:20201022T093000Z DTEND:20201022T103000Z DTSTAMP:20260422T212705Z UID:WOPARA/10 DESCRIPTION:Title: Nonlinear boundary value problems in connexion with harmonic functions \nby Laurent Véron (Universite de tour\, France) as part of Webinar on PD E and related areas\n\n\nAbstract\nWe study the problem of finding a funct ionuverifying−∆u= 0 inΩ under the boundary condition∂u∂n+g(u) = μon∂Ω where Ω⊂RNis a smoothdomain\,nis the normal unit outward ve ctor to Ω\,μis a measure on∂Ω andga continuous nondecreasing functi on. We give sufficient condition ongfor thisproblem to be solvable for an y measure. Wheng(r) =|r|p−1r\,p >1\, we giveconditions in order an isol ated singularity on∂Ω to be removable. We also givecapacitary conditi ons on a measureμin order the problem withg(r) =|r|p−1rto be solvable f or someμ. We also study the isolated singularities of functionssatisfyin g−∆u= 0inΩ and∂u∂n+g(u) = 0 on∂Ω\\{0}.\n LOCATION:https://researchseminars.org/talk/WOPARA/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Stefano Bianchini (SISSA\, Trieste\, Italy) DTSTART:20201027T093000Z DTEND:20201027T103000Z DTSTAMP:20260422T212705Z UID:WOPARA/11 DESCRIPTION:Title: On the sticky particle solutions to the multi-dimensional pressureless Eul er equations\nby Stefano Bianchini (SISSA\, Trieste\, Italy) as part o f Webinar on PDE and related areas\n\n\nAbstract\nAbstract: In this talk we consider the multi-dimensional pressureless Eulersystem and we tackle t he problem of existence and uniqueness of sticky particlesolutions for gen eral measure-type initial data. Although explicit counterexam-ples to bot h existence and uniqueness are known\, the problem of whether onecan still find sticky particle solutions for a large set of data and of how one can select them was up to our knowledge still completely open. In this talk w e provethat for a comeager set of initial data in the weak topology the pr essureless Eu-ler system admits a unique sticky particle solution given by a free flow wheretrajectories are disjoint straight lines. Indeed\, suc h an existence and unique-ness result holds for a broader class of solutio ns decreasing their kinetic energy\,which we call dissipative solutions\, and which turns out to be the compact weakclosure of the classical sticky particle solutions. Therefore any scheme for whichthe energy is l.s.c. a nd is dissipated will converge\, for a comeager set of data\,to our soluti on\, i.e. the free flow\n LOCATION:https://researchseminars.org/talk/WOPARA/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Guy Vallet (University of Pau\, France) DTSTART:20201029T093000Z DTEND:20201029T103000Z DTSTAMP:20260422T212705Z UID:WOPARA/12 DESCRIPTION:Title: Lewy-Stampacchia’s inequalities\nby Guy Vallet (University of Pau\, France) as part of Webinar on PDE and related areas\n\n\nAbstract\nThis ta lk will be about obstacle problems for elliptic\, parabolic and stochastic problems\, based on the proof\, and use\, of Lewy-Stampacchia’s inequal ities.\n LOCATION:https://researchseminars.org/talk/WOPARA/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Plamen Stefanov (Purdue University West Lafayette\, USA.) DTSTART:20201103T150000Z DTEND:20201103T160000Z DTSTAMP:20260422T212705Z UID:WOPARA/13 DESCRIPTION:Title: Local and global boundary rigidity\nby Plamen Stefanov (Purdue Univers ity West Lafayette\, USA.) as part of Webinar on PDE and related areas\n\n \nAbstract\nThe boundary rigidity problem consist of recovering a Riemanni an metric in a domain\, up to an isometry\, from the distance b etween boundary points. We show that in dimensions three and hig her\, knowing the distance near a fixed strictly convex boundary point allows us to reconstruct the metric inside the domain near that point\, an d that this reconstruction is stable. We also prove semi-global and g lobal results under certain an assumption of the existence of a strictly convex foliation. The problem can be reformulated asa r ecovery of the metric from the arrival times of waves between b oundary points\; which is known as travel-time tomography. The interest i n this problem is motivated by imaging problems in seismology: to recover the sub-surface structure of the Earth given travel-times from the propagation of seismic waves. In oil exploration\, the seismic signals are man-made and the problem is local innature. In particular\, we can r ecover locally the compressional and the shearwave speeds for the elastic Earth model\, given local information. The talk is based on joint work w ith G.Uhlmann (UW) and A.Vasy (Stanford). We will alsopresent results for a recovery of a Lorentzian metric from red shifts motivatedby the problem of observing cosmic strings.\n LOCATION:https://researchseminars.org/talk/WOPARA/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Itai Shafrir (Technion\, Israel Institute of Technology\, Israel.) DTSTART:20201105T093000Z DTEND:20201105T103000Z DTSTAMP:20260422T212705Z UID:WOPARA/14 DESCRIPTION:Title: Minimizers of a variational problem for nematic liquid crystals with varia ble degree of orientation in two dimensions\nby Itai Shafrir (Technion \, Israel Institute of Technology\, Israel.) as part of Webinar on PDE and related areas\n\n\nAbstract\nWe study the asymptotic behavior\, when k→ ∞\, of the minimizers of the energy Gk(u)=∫_Ω((k−1)|(∇|u|)|^2+| ∇u|^2)\, over the class of maps u∈H^1(Ω\, R2) satisfying the boundar y condition u=g on ∂Ω\, where Ω is a smooth\, bounded and simply co nnected domain in R^2 and g:∂Ω→S^1. The motivation comes from a sim plified version of Ericksen model for nematic liquid crystals. We will pr esent similarities and differences with respect to the analog problem for the Ginzburg-Landau energy.\n\nBased on a joint work with Dmitry Golovaty. \n LOCATION:https://researchseminars.org/talk/WOPARA/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Michel Chipot (University of Zurich\, Switzerland) DTSTART:20201110T093000Z DTEND:20201110T103000Z DTSTAMP:20260422T212705Z UID:WOPARA/15 DESCRIPTION:Title: PROPAGATION OF INTERACTING SPECIES IN A SPECIAL ENVIRONMENT\nby Michel Chipot (University of Zurich\, Switzerland) as part of Webinar on PDE and related areas\n\n\nAbstract\n$\\href{https://www.iitk.ac.in/math/data/Chi pot-abstract.pdf}{\\text{click here for abstract}}$\n LOCATION:https://researchseminars.org/talk/WOPARA/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Moshe Marcus (Technion\, Israel Institute of Technology\, Israel.) ) DTSTART:20201112T093000Z DTEND:20201112T103000Z DTSTAMP:20260422T212705Z UID:WOPARA/16 DESCRIPTION:Title: Boundary value problems for Schrodinger equations with Hardy type potentia ls\nby Moshe Marcus (Technion\, Israel Institute of Technology\, Israe l.)) as part of Webinar on PDE and related areas\n\n\nAbstract\nWe conside r equations of the form− $L_V u=\\tau$ where $L_V= \\Delta +V$ and $\\ta u$ is a Radon measure in a Lipschitz bounded domain $D\\subset\\mathbb{R}^ N$. The assumptions on $V$ include the condition $|V(x)|\\leq a \\delta ( x)^{-2}$ - where $a >0$ and $\\delta (x) = \\mbox{dist} (x\,\\partial D)$. An additional condition guarantees the existence of a ground state $\\Phi _V$. The model example is $V=\\gamma \\delta (x)^{-2}$ where $\\gamma< cH$ ($cH$=Hardy constant). \n\nFor positive solutions of the equation we defi ne the $L_V$ boundary trace. If $\\int_D \\Phi_V d\\tau<\\infty$\, the bou ndary trace is well defined as a positive\, bounded measure $\\nu$ on $\\p artial D$. We consider the corresponding b.v.p.\, namely\, $-L+V u=\\tau$ in $D$\,$u=\\nu$ on $\\partial D$. We show that\, for $\\tau$ and $\\nu$ as above\, the b.v.p. has a unique solution. Further\, under some co nditions on the ground state -satisfied for a large family of potenti als - we obtain sharp two sided estimates of positive solutions of the b.v .p. Finally we discuss some applications to semilinear problems involving the operator $L_V$.\n LOCATION:https://researchseminars.org/talk/WOPARA/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Xavier Ros-Oton (University of Zurich\, Switzerland) DTSTART:20201117T093000Z DTEND:20201117T103000Z DTSTAMP:20260422T212705Z UID:WOPARA/17 DESCRIPTION:Title: The Neumann problem for the fractional Laplacian\nby Xavier Ros-Oton ( University of Zurich\, Switzerland) as part of Webinar on PDE and related areas\n\n\nAbstract\n$\\href{https://www.iitk.ac.in/math/data/xavier-abstr act.pdf}{\\text{click here for abstract}}$\n LOCATION:https://researchseminars.org/talk/WOPARA/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Giampiero Palatucci (University of Parma\, Italy) DTSTART:20201119T093000Z DTEND:20201119T103000Z DTSTAMP:20260422T212705Z UID:WOPARA/18 DESCRIPTION:Title: Holder regularity for nonlocal double phase equations\nby Giampiero Pa latucci (University of Parma\, Italy) as part of Webinar on PDE and relate d areas\n\n\nAbstract\n$\\href{https://www.iitk.ac.in/math/data/Palatucci- Abstract.pdf}{\\text{click here for abstract}}$\n LOCATION:https://researchseminars.org/talk/WOPARA/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Enrico Valdinoci (University of western Australia\, Australia) DTSTART:20201124T093000Z DTEND:20201124T103000Z DTSTAMP:20260422T212705Z UID:WOPARA/19 DESCRIPTION:Title: Boundary behavior of nonlocal minimal surfaces\nby Enrico Valdinoci (U niversity of western Australia\, Australia) as part of Webinar on PDE and related areas\n\n\nAbstract\n$\\href{https://www.iitk.ac.in/math/data/vald inoci-Abstract.pdf}{\\text{click here for abstract}}$\n LOCATION:https://researchseminars.org/talk/WOPARA/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Martina Hofmanova (Bielefeld University\, Germany) DTSTART:20201126T093000Z DTEND:20201126T103000Z DTSTAMP:20260422T212705Z UID:WOPARA/20 DESCRIPTION:Title: On ill- and well-posedness of dissipative martingale solutions to stochast ic 3D Euler equations\nby Martina Hofmanova (Bielefeld University\, Ge rmany) as part of Webinar on PDE and related areas\n\n\nAbstract\n$\\href{ https://www.iitk.ac.in/math/data/martina-Abstract.pdf}{\\text{click here f or abstract}}$\n LOCATION:https://researchseminars.org/talk/WOPARA/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Manjunath Krishnapur (Indian Institute of Science\, India) DTSTART:20201201T093000Z DTEND:20201201T103000Z DTSTAMP:20260422T212705Z UID:WOPARA/21 DESCRIPTION:Title: The random plane wave and related objects\nby Manjunath Krishnapur (In dian Institute of Science\, India) as part of Webinar on PDE and related a reas\n\n\nAbstract\n$\\href{https://www.iitk.ac.in/math/data/Manjunath-abs tract.pdf}{\\text{click here for abstract}}$\n LOCATION:https://researchseminars.org/talk/WOPARA/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Arick Shao (Queen Mary University of London\, United Kingdom) DTSTART:20201203T093000Z DTEND:20201203T103000Z DTSTAMP:20260422T212705Z UID:WOPARA/22 DESCRIPTION:Title: Controllability of Waves and Geometric Carleman Estimates\nby Arick Sh ao (Queen Mary University of London\, United Kingdom) as part of Webinar o n PDE and related areas\n\n\nAbstract\n$\\href{https://www.iitk.ac.in/math /data/Arick-abstract.pdf}{\\text{click here for abstract}}$\n LOCATION:https://researchseminars.org/talk/WOPARA/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Gyula Csato (University of Barcelona\, Spain) DTSTART:20201208T093000Z DTEND:20201208T103000Z DTSTAMP:20260422T212705Z UID:WOPARA/23 DESCRIPTION:Title: Fractional Michael-Simon Sobolev inequalities\nby Gyula Csato (Univers ity of Barcelona\, Spain) as part of Webinar on PDE and related areas\n\n\ nAbstract\n$\\href{https://www.iitk.ac.in/math/data/Gyula-abstract.pdf}{\\ text{click here for abstract}}$\n LOCATION:https://researchseminars.org/talk/WOPARA/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Luca Esposito (University of Salerno\, Italy) DTSTART:20201210T093000Z DTEND:20201210T103000Z DTSTAMP:20260422T212705Z UID:WOPARA/24 DESCRIPTION:Title: Density lower bound estimate for local minimizers of free interface proble m with volume constraint\nby Luca Esposito (University of Salerno\, It aly) as part of Webinar on PDE and related areas\n\n\nAbstract\n$\\href{ht tps://www.iitk.ac.in/math/data/Luca_Esposito-abstract.pdf}{\\text{click he re for abstract}}$\n LOCATION:https://researchseminars.org/talk/WOPARA/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Sylvain Ervedoza (Institut de Mathématiques de Bordeaux\, Univers ité de Bordeaux\, France) DTSTART:20201215T093000Z DTEND:20201215T103000Z DTSTAMP:20260422T212705Z UID:WOPARA/25 DESCRIPTION:by Sylvain Ervedoza (Institut de Mathématiques de Bordeaux\, Université de Bordeaux\, France) as part of Webinar on PDE and related ar eas\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/WOPARA/25/ END:VEVENT END:VCALENDAR