Travelling Waves in Partially Degenerate Reaction-Diffusion Systems

B. Kazmierczak; V. Volpert

Mathematical Modelling of Natural Phenomena (2010)

  • Volume: 2, Issue: 2, page 106-125
  • ISSN: 0973-5348

Abstract

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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.

How to cite

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Kazmierczak, B., and Volpert, V.. "Travelling Waves in Partially Degenerate Reaction-Diffusion Systems." Mathematical Modelling of Natural Phenomena 2.2 (2010): 106-125. <http://eudml.org/doc/222233>.

@article{Kazmierczak2010,
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. },
author = {Kazmierczak, B., Volpert, V.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {travelling waves; reaction-diffusion systems; calcium dynamics},
language = {eng},
month = {3},
number = {2},
pages = {106-125},
publisher = {EDP Sciences},
title = {Travelling Waves in Partially Degenerate Reaction-Diffusion Systems},
url = {http://eudml.org/doc/222233},
volume = {2},
year = {2010},
}

TY - JOUR
AU - Kazmierczak, B.
AU - Volpert, V.
TI - Travelling Waves in Partially Degenerate Reaction-Diffusion Systems
JO - Mathematical Modelling of Natural Phenomena
DA - 2010/3//
PB - EDP Sciences
VL - 2
IS - 2
SP - 106
EP - 125
AB - 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.
LA - eng
KW - travelling waves; reaction-diffusion systems; calcium dynamics
UR - http://eudml.org/doc/222233
ER -

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