Stability of nonconstant stationary solutions in a reaction-diffusion equation coupled to the system of ordinary differential equations

Yuriy Golovaty, Anna Marciniak-Czochra, Mariya Ptashnyk

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

In this paper we study pattern formation arising in a system of a single reaction-diffusion equation coupled with subsystem of ordinary differential equations, describing spatially-distributed growth of clonal populations of precancerous cells, whose proliferation is controlled by growth factors diffusing in the extracellular medium and binding to the cell surface. We extend the results on the existence of nonhomogenous stationary solutions obtained in [9] to a general Hill-type production function and full parameter set. Using spectral analysis and perturbation theory we derive conditions for the linearized stability of such spatial patterns.

Original languageEnglish
Pages (from-to)229-241
Number of pages13
JournalCommunications on Pure and Applied Analysis
Volume11
Issue number1
DOIs
Publication statusPublished - 2012

Keywords

  • Linearized stability
  • Pattern formation
  • Reaction-diffusion equations
  • Spectral analysis

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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