Issue |
Math. Model. Nat. Phenom.
Volume 2, Number 2, 2007
Reaction-diffusion waves
|
|
---|---|---|
Page(s) | 106 - 125 | |
DOI | https://doi.org/10.1051/mmnp:2008021 | |
Published online | 15 June 2008 |
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.