Type II blow-up mechanisms in a semilinear heat equation with critical Joseph–Lundgren exponent

Yukihiro Seki

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

We are concerned with blow-up mechanisms in a semilinear heat equation ut=Δu+|u|p−1u,x∈RN,t>0, where p>1 is a constant. It is well known that type II blow-up does occur if N≥11 and p>pJL, where pJL stands for the Joseph–Lundgren exponent: pJL={+∞,N≤10,1+[Formula presented],N≥11. On the other hand, it is also known that, if p<pJL, type II blow-up cannot occur under mild assumptions on initial data as far as nonnegative radially symmetric solutions are concerned. It has long remained open whether or not type II blow-up occurs for the borderline case p=pJL,N≥11. In the present article we prove constructively the existence of type II blow-up solutions for the Joseph–Lundgren critical case, thus giving an answer to this question.

Original languageEnglish
Pages (from-to)3380-3456
Number of pages77
JournalJournal of Functional Analysis
Volume275
Issue number12
DOIs
Publication statusPublished - Dec 15 2018

All Science Journal Classification (ASJC) codes

  • Analysis

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