On the initial-boundary value problem for some quasilinear parabolic equations of divergence form

Mitsuhiro Nakao

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5 Citations (Scopus)


In this paper we give an existence theorem of global classical solution to the initial boundary value problem for the quasilinear parabolic equations of divergence form ut−div{σ(|∇u|2)∇u}=f(∇u,u,x,t) where σ(|∇u|2) may not be bounded as |∇u|→∞. As an application the logarithmic type nonlinearity σ(|∇u|2)=log⁡(1+|∇u|2) which is growing as |∇u|→∞ and degenerate at |∇u|=0 is considered under f≡0.

Original languageEnglish
Pages (from-to)8565-8580
Number of pages16
JournalJournal of Differential Equations
Issue number12
Publication statusPublished - 2017 Dec 15
Externally publishedYes



  • Growing nonlinearity
  • Moser's method
  • Quasilinear parabolic equation

ASJC Scopus subject areas

  • Analysis

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