Blowup for a fourth-order parabolic equation with gradient nonlinearity

Kazuhiro Ishige, Nobuhito Miyake, Shinya Okabe

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)927-953
Number of pages27
JournalSIAM Journal on Mathematical Analysis
Volume52
Issue number1
DOIs
Publication statusPublished - 2020

Keywords

  • blowup
  • epitaxial growth
  • fourth-order parabolic equation
  • gradient nonlinearity

ASJC Scopus subject areas

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

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