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SUMMARY:Fernando Quirós (Universidad Autónoma de Madrid)
DTSTART:20210930T130000Z
DTEND:20210930T140000Z
DTSTAMP:20260423T035824Z
UID:SNPDEA/35
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SNPDEA/35/">
 Travelling-wave behaviour in problems with degenerate diffusion</a>\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/
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