Stability of patterns and of constant steady states for a cross-diffusion system

G. Svantnerné Sebestyén, I. Faragó, Róbert Horváth, R. Kersner, M. Klincsik

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

This paper considers mathematical and numerical models of normal and abnormal tissue growth. To this aim, we analyse a nonlinear system of partial differential equations, called as cross-diffusion system, in a rather general form. We investigate the dynamics of the system in dependence on the system parameters. We show analytically the existence of a periodic stationary solution for the set of certain positive initial data. The other choices of the parameters are investigated by construction of corresponding numerical models. We also analyse the stability of the stationary solutions. Numerical examples demonstrate our results.

Original languageEnglish
Pages (from-to)208-216
Number of pages9
JournalJournal of Computational and Applied Mathematics
Volume293
DOIs
Publication statusPublished - Jan 22 2015

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Cross-diffusion System
Stationary Solutions
Numerical models
Systems of Partial Differential Equations
Partial differential equations
Nonlinear systems
Nonlinear Systems
Mathematical Model
Tissue
Mathematical models
Numerical Examples
Demonstrate

Keywords

  • Cross-diffusion
  • Nonlinear systems of PDEs
  • Periodic solutions
  • Stability of patterns

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

Cite this

Stability of patterns and of constant steady states for a cross-diffusion system. / Sebestyén, G. Svantnerné; Faragó, I.; Horváth, Róbert; Kersner, R.; Klincsik, M.

In: Journal of Computational and Applied Mathematics, Vol. 293, 22.01.2015, p. 208-216.

Research output: Contribution to journalArticle

Sebestyén, G. Svantnerné ; Faragó, I. ; Horváth, Róbert ; Kersner, R. ; Klincsik, M. / Stability of patterns and of constant steady states for a cross-diffusion system. In: Journal of Computational and Applied Mathematics. 2015 ; Vol. 293. pp. 208-216.
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