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

Mostafa Bendahmane | Zendy; Kenneth H. Karlsen | Zendy

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

Author(s) -

Mostafa Bendahmane,

Kenneth H. Karlsen

Publication year - 2006

Publication title -

networks and heterogeneous media

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.732

H-Index - 34

eISSN - 1556-181X

pISSN - 1556-1801

DOI - 10.3934/nhm.2006.1.185

Subject(s) - degenerate energy levels , reaction–diffusion system , uniqueness , diffusion , class (philosophy) , mathematical analysis , physics , bidomain model , mathematics , computer science , thermodynamics , quantum mechanics , artificial intelligence

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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