Nonlinear pseudoparabolic equations as singular limit of reaction-diffusion equations

Mariya Ptashnyk (Lead / Corresponding author)

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

In this article, a solution of a nonlinear pseudoparabolic equation is constructed as a singular limit of a sequence of solutions of quasilinear hyperbolic equations. If a system with cross diffusion, modelling the reaction and diffusion of two biological, chemical, or physical substances, is reduced then such an hyperbolic equation is obtained. For regular solutions even uniqueness can be shown, although the needed regularity can only be proved in two dimensions.
Original languageEnglish
Pages (from-to)1285-1299
Number of pages15
JournalApplicable Analysis
Volume85
Issue number10
DOIs
Publication statusPublished - Oct 2006

Keywords

  • Pseudo-parabolic equations
  • Galerkin’s method
  • Reaction-diffusion equations

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