ON exact dead-core rates for a semilinear heat equation with strong absorption

Yukihiro Seki

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

We study a semilinear heat equation with strong absorption ut = u - up with 0 < p < 1 in RN. A solution is known to develop dead-core in finite time for a wide class of initial data. We construct specific solutions with exact dead-core rates faster than the one given by the corresponding ODE. They are constructed formally by means of matched asymptotic expansion technique and rigorously by means of topological fixed-point arguments based on a priori estimates. To obtain the a priori estimates, we analyze a certain linearized problem in a new function space $\mathcal{H}'$.

Original languageEnglish
Pages (from-to)1-52
Number of pages52
JournalCommunications in Contemporary Mathematics
Volume13
Issue number1
DOIs
Publication statusPublished - Feb 1 2011

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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