Asymptotics for nonlinear heat equations

Nakao Hayashi, Pavel I. Naumkin

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We study the Cauchy problem for the nonlinear heat equation ut-Δu+u1+σ=0,x∈Rn,t>0,u(0,x)=u0(x),x∈Rn, in the sub critical case of σ∈(0,2n). In the present paper we intend to give a more precise estimate for the remainder term in the asymptotic representation known from paper Escobedo and Kavian (1987) [5]u(t,x)=t-1σw0(xt)+o(t- 1σ) as t→∞ uniformly with respect to x∈Rn, where w0(ξ) is a positive solution of equation -Δw-ξ2·∇w+w1+σ= 1σw which decays rapidly at infinity: lim|ξ|→±∞|ξ |2σw0(ξ)=0.

Original languageEnglish
Pages (from-to)1585-1595
Number of pages11
JournalNonlinear Analysis, Theory, Methods and Applications
Volume74
Issue number5
DOIs
Publication statusPublished - 2011 Mar 1
Externally publishedYes

Keywords

  • Asymptotics of solutions
  • Nonlinear heat equations

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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