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

Mitsuhiro Nakao

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

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
Volume263
Issue number12
DOIs
Publication statusPublished - 2017 Dec 15
Externally publishedYes

Fingerprint

Global Classical Solution
Quasilinear Parabolic Equations
Existence Theorem
Initial-boundary-value Problem
Boundary value problems
Divergence
Logarithmic
Nonlinearity
Form

Keywords

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

ASJC Scopus subject areas

  • Analysis

Cite this

On the initial-boundary value problem for some quasilinear parabolic equations of divergence form. / Nakao, Mitsuhiro.

In: Journal of Differential Equations, Vol. 263, No. 12, 15.12.2017, p. 8565-8580.

Research output: Contribution to journalArticle

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