*Math. Model. Nat. Phenom.*Vol. 2, No.2, 2007, pp. 106-125

## Travelling Waves in Partially Degenerate Reaction-Diffusion Systems

^{1}
Institute of Fundamental Technological Research, PAS, Warsaw

^{2}
Department of Mathematics, UMR 5208 CNRS, Université Lyon 1
69622 Villeurbanne, France

Corresponding author: bkazmier@ippt.gov.pl

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.

Mathematics Subject Classification: 34A34 / 35K57

Key words: travelling waves / reaction-diffusion systems / calcium dynamics

*© EDP Sciences, 2007*