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SUMMARY:Jesús Ildefonso Díaz (Universidad Complutense de Madrid\,)
DTSTART:20200601T083500Z
DTEND:20200601T092500Z
DTSTAMP:20260416T001647Z
UID:Veron/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Veron/2/">Be
 yond the unique continuation: "flat solutions" for reactive slow diffusion
  and the confinement singular potentials for the Schrodinger equation</a>\
 nby Jesús Ildefonso Díaz (Universidad Complutense de Madrid\,) as part o
 f Singular Problems Associated to Quasilinear Equations\, June 1-3\, 2020\
 n\n\nAbstract\nSolutions with compact support for some nonlinear\nelliptic
  and parabolic equations\, and many other free boundary problems\, are\nfo
 rmulations for which the Unique Continuation Principle\, in its several\nv
 ersions\, fails. In such problems (which have attracted the attention of\n
 M.F. Bidaut-Veron\, L. Veron\, and many other specialists) the solution $u
 $\nand its normal derivative vanish on a region of the boundary (which lea
 ds to\nthe definition of a \\textquotedblleft flat solution\\textquotedblr
 ight\\ of\nthe corresponding equation).\n\nIn this talk I will present\, i
 n a very sketched way\, some recent results in\nthis direction\, trying to
  show how many open problems of this nature still\nremain as a source of c
 urrent research.\n\nMore specifically\, I will report on some results conc
 erning the following\nproblems:\n\nI) Stable flat solutions of $u_{t}-\\De
 lta u^{m}+u^{a}=\\lambda u^{b}$\nfor $0 < a < b < m$ under the stability c
 ondition $2(m+a)(m+b)-N(m-a)(m-b) < 0$\n(joint work with J.~Hern\\'{a}ndez
  and Y. Sh.~Ilyasov)\,\n\nII) Flat solutions to $\\mathbf{i}\\frac{\\parti
 al \\mathbf{\\psi }}{\\partial t}%\n=-\\Delta \\mathbf{\\psi }+V(x)\\mathb
 f{\\psi }$ in $\\mathbb{R}^{N}\,$ for $%\nV(x)\\geq Cd(x\,\\partial \\Omeg
 a )^{-\\alpha }\,$ with $\\alpha \\geq 2$\, for a\ngiven bounded domain $\
 \Omega $ (my own research\, continued in collaboration\nwith J. M. Rakotos
 on\, D. G\\'{o}mez-Castro\, R. Temam and J. L. V\\'{a}zquez).\n\nHere is t
 he poster of this talk: \nhttps://www.dropbox.com/s/fnyc0kyf975xlq4/Poster
 %20Workshop.pdf?dl=0\n\nPlease visit our website to get more information:\
 nhttps://nguyenquochung1241.wixsite.com/qhung/post/singular-problems-assoc
 iated-to-quasilinear-equations-june-1-3-2020\n
LOCATION:https://researchseminars.org/talk/Veron/2/
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