Global existence and gradient estimates for the quasilinear parabolic equations of m-Laplacian type with a nonlinear convection term

Mitsuhiro Nakao, Caisheng Chen

Research output: Contribution to journalArticle

27 Citations (Scopus)

Abstract

In this paper, we derive precise estimates for ∇u(t) including smoothing effects near t=0 and decay as t→∞ as well as global existence of the solutions u(t) to the initial-boundary value problem in a bounded domain in Rn for the quasilinear parabolic equation of the m Laplacian type with a nonlinear convection term b(u)∇u. For the initial data u0 we only assume u0∈Lq(Ω), 1≤q<∞.

Original languageEnglish
Pages (from-to)224-250
Number of pages27
JournalJournal of Differential Equations
Volume162
Issue number1
DOIs
Publication statusPublished - 2000 Mar 20
Externally publishedYes

Keywords

  • Convection
  • Global existence
  • Gradient estimate
  • Quasilinear parabolic equation

ASJC Scopus subject areas

  • Analysis

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