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

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    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 - Jan 2012

    Keywords

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

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