Blowup for a fourth-order parabolic equation with gradient nonlinearity

Kazuhiro Ishige, Nobuhito Miyake, Shinya Okabe

研究成果: Article査読

抄録

Let u be a solution to the Cauchy problem for a fourth-order nonlinear parabolic equation tu+(-δ)2u =-(u|p-2u) on RN, where p 2 and N 1. In this paper we give a sufficient condition for the maximal existence time TM(u) of the solution u to be finite. Furthermore, we show that if TM(u) ∞, then u(t) L∞(RN) blows up at t = TM(u), and we obtain lower estimates on the blow-up rate. We also give a sufficient condition on the existence of global-in-Time solutions to the Cauchy problem.

本文言語English
ページ(範囲)927-953
ページ数27
ジャーナルSIAM Journal on Mathematical Analysis
52
1
DOI
出版ステータスPublished - 2020

ASJC Scopus subject areas

  • 分析
  • 計算数学
  • 応用数学

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