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

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March 2006, 1(1): 185-218. doi: 10.3934/nhm.2006.1.185

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

Mostafa Bendahmane ^1, and Kenneth H. Karlsen ^1,

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

Received September 2005 Revised November 2005 Published January 2006

Abstract
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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.

Keywords: existence, weak solution, uniqueness, bidomain model, Reaction-diffusion system, degenerate, cardiac electric ﬁeld..

Mathematics Subject Classification: Primary: 35K57, 35M10; Secondary: 35A0.

Citation: Mostafa Bendahmane, Kenneth H. Karlsen. Analysis of a class of degenerate reaction-diffusion systems and the bidomain model of cardiac tissue. Networks & Heterogeneous Media, 2006, 1 (1) : 185-218. doi: 10.3934/nhm.2006.1.185

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