Nonlinear pseudoparabolic equations as singular limit of reaction-diffusion equations

Mariya Ptashnyk (Lead / Corresponding author)

Research output: Contribution to journalArticle

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

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Quasilinear Hyperbolic Equation
Pseudoparabolic Equations
Cross-diffusion
Singular Limit
Regular Solution
Hyperbolic Equations
Reaction-diffusion Equations
Nonlinear equations
Two Dimensions
Nonlinear Equations
Uniqueness
Regularity
Modeling

Keywords

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

Cite this

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Nonlinear pseudoparabolic equations as singular limit of reaction-diffusion equations. / Ptashnyk, Mariya (Lead / Corresponding author).

In: Applicable Analysis, Vol. 85, No. 10, 10.2006, p. 1285-1299.

Research output: Contribution to journalArticle

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