Upper estimates for blow-up solutions of a quasi-linear parabolic equation

Koichi Anada, Tetsuya Ishiwata, Takeo Ushijima

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we consider a quasi-linear parabolic equation ut= up(xxx+ u) . It is known that there exist blow-up solutions and some of them develop Type II singularity. However, only a few results are known about the precise behavior of Type II blow-up solutions for p> 2 . We investigated the blow-up solutions for the equation with periodic boundary conditions and derived upper estimates of the blow-up rates in the case of 2 < p< 3 and in the case of p= 3 , separately. In addition, we assert that if 2 ≤ p≤ 3 then limt↗T(T-t)1p+εmaxu(x,t)=0 z for any ε> 0 under some assumptions.

Original languageEnglish
Pages (from-to)381-405
Number of pages25
JournalJapan Journal of Industrial and Applied Mathematics
Volume41
Issue number1
DOIs
Publication statusPublished - 2024 Jan

Keywords

  • Asymptotic behavior
  • Blow-up phenomena
  • Quasi-linear parabolic equation

ASJC Scopus subject areas

  • General Engineering
  • Applied Mathematics

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