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

Koichi Anada, Tetsuya Ishiwata, Takeo Ushijima

研究成果: Article査読

抄録

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.

本文言語English
ページ(範囲)381-405
ページ数25
ジャーナルJapan Journal of Industrial and Applied Mathematics
41
1
DOI
出版ステータスPublished - 2024 1月

ASJC Scopus subject areas

  • 工学一般
  • 応用数学

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