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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, and
Kenneth H. Karlsen^1,

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

Received: September 2005

Revised: November 2005

Published: March 2006

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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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Mathematics Subject Classification: Primary: 35K57, 35M10; Secondary: 35A05.

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