Nonlinear Diffusion Equations on Unbounded Fractal Domains

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22 Citations (Scopus)

Abstract

We investigate the nonlinear diffusion equation partial derivativeu/partial derivativet Deltau + up, p > 1, on certain unbounded fractal domains, where Delta is the infinitesimal generator of the semigroup associated with a corresponding heat kernel. We show that there are nonnegative global solutions for non-negative initial data if p > If 2/d(s), while solutions blow up if p less than or equal to 1 + 2/d(s), where d(s) is the spectral dimension of the domain. We investigate smoothness and Holder continuity of solutions when they exist. (C) 2001 Academic Press.

Original languageEnglish
Pages (from-to)606-624
Number of pages19
JournalJournal of Mathematical Analysis and Applications
Volume256
Issue number2
DOIs
Publication statusPublished - 15 Apr 2001

Keywords

  • BROWNIAN-MOTION

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