A solution of nonlinear diffusion problems by semilinear reaction-diffusion systems

Hideki Murakawa

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1 Citation (Scopus)

Abstract

This paper deals with nonlinear diffusion problems involving degenerate parabolic problems, such as the Stefan problem and the porous medium equation, and cross-diffusion systems in population ecology. The degeneracy of the diffusion and the effect of crossdiffusion, that is, nonlinearities of the diffusion, complicate its analysis. In order to avoid the nonlinearities, we propose a reaction-diffusion system with solutions that approximate those of the nonlinear diffusion problems. The reaction-diffusion system includes only a simple reaction and linear diffusion. Resolving semilinear problems is typically easier than dealing with nonlinear diffusion problems. Therefore, our ideas are expected to reveal new and more effective approaches to the study of nonlinear problems.

Original languageEnglish
Pages (from-to)580-590
Number of pages11
JournalKybernetika
Volume45
Issue number4
Publication statusPublished - 2009
Externally publishedYes

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All Science Journal Classification (ASJC) codes

  • Software
  • Artificial Intelligence
  • Control and Systems Engineering
  • Information Systems
  • Theoretical Computer Science
  • Electrical and Electronic Engineering

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