Nonlinear diffusion equations driven by the p(·)-Laplacian

Goro Akagi, Kei Matsuura

Research output: Contribution to journalArticlepeer-review

23 Citations (Scopus)

Abstract

This paper is concerned with nonlinear diffusion equations driven by the p(·)-Laplacian with variable exponents in space. The well-posedness is first checked for measurable exponents by setting up a subdifferential approach. The main purposes are to investigate the large-time behavior of solutions as well as to reveal the limiting behavior of solutions as p(·) diverges to the infinity in the whole or in a subset of the domain. To this end, the recent developments in the studies of variable exponent Lebesgue and Sobolev spaces are exploited, and moreover, the spatial inhomogeneity of variable exponents p(·) is appropriately controlled to obtain each result.

Original languageEnglish
Pages (from-to)37-64
Number of pages28
JournalNonlinear Differential Equations and Applications
Volume20
Issue number1
DOIs
Publication statusPublished - 2013 Feb
Externally publishedYes

Keywords

  • Nonlinear diffusion
  • Parabolic equation
  • Sobolev spaces
  • Subdifferential
  • Variable exponent Lebesgue
  • p(·)-Laplacian

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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