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

Murakawa Hldeki Murakawa

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


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
Issue number4
Publication statusPublished - 2009
Externally publishedYes

All Science Journal Classification (ASJC) codes

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


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