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Travelling Waves in Partially DegenerateReaction-Diffusion Systems

Published online by Cambridge University Press:  15 June 2008

B. Kazmierczak  and
V. Volpert
B. Kazmierczak*
Affiliation:
Institute of Fundamental Technological Research, PAS, Warsaw
V. Volpert
Affiliation:
Department of Mathematics, UMR 5208 CNRS, Université Lyon 1 69622 Villeurbanne, France
*
bkazmier@ippt.gov.pl
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Abstract

We study the existence and some properties of travelling waves in partially degenerate reaction-diffusion systems. Such systems may for example describe intracellular calcium dynamics in the presence of immobile buffers. In order to prove the wave existence, we first consider the non degenerate case and then pass to the limit as some of the diffusion coefficient converge to zero. The passage to the limit is based on a priori estimates of solutions independent of the values of the diffusion coefficients. The wave uniqueness is also proved.

Keywords

travelling wavesreaction-diffusion systemscalcium dynamics
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 2 , Issue 2: Reaction-diffusion waves , 2007 , pp. 106 - 125
Copyright
© EDP Sciences, 2007

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