Analysis of a class of degenerate reaction-diffusion systems and the bidomain model of cardiac tissue

Mostafa Bendahmane; Kenneth H. Karlsen; Mostafa Bendahmane; Kenneth H. Karlsen

doi:10.3934/nhm.2006.1.185

Networks and Heterogeneous Media

2006, Volume 1, Issue 1: 185-218. doi: 10.3934/nhm.2006.1.185

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Analysis of a class of degenerate reaction-diffusion systems and the bidomain model of cardiac tissue

Mostafa Bendahmane ^{1
,},
Kenneth H. Karlsen ^{1
,}

1.
Centre of Mathematics for Applications, University of Oslo, P.O. Box 1053, Blindern, N–0316 Oslo

Received: 01 September 2005 Revised: 01 November 2005
Primary: 35K57, 35M10; Secondary: 35A05.

We prove well-posedness (existence and uniqueness) results for a class of degenerate reaction-diffusion systems. A prototype system belonging to this class is provided by the bidomain model, which is frequently used to study and simulate electrophysiological waves in cardiac tissue. The existence result, which constitutes the main thrust of this paper, is proved by means of a nondegenerate approximation system, the Faedo-Galerkin method, and the compactness method.
- Reaction-diffusion system,
- degenerate,
- weak solution,
- existence,
- uniqueness,
- bidomain model,
- cardiac electric ﬁeld
Citation: Mostafa Bendahmane, Kenneth H. Karlsen. Analysis of a class of degenerate reaction-diffusion systems and the bidomain model of cardiac tissue[J]. Networks and Heterogeneous Media, 2006, 1(1): 185-218. doi: 10.3934/nhm.2006.1.185

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Abstract

We prove well-posedness (existence and uniqueness) results for a class of degenerate reaction-diffusion systems. A prototype system belonging to this class is provided by the bidomain model, which is frequently used to study and simulate electrophysiological waves in cardiac tissue. The existence result, which constitutes the main thrust of this paper, is proved by means of a nondegenerate approximation system, the Faedo-Galerkin method, and the compactness method.
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