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

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

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Original languageEnglish
Pages229-241
Number of pages13
JournalCommunications on Pure and Applied Analysis
Journal publication dateJan 2012
Journal number1
Volume11
DOIs
StatePublished

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.

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