A Coupled System of PDEs and ODEs Arising in Electrocardiograms Modeling | Zendy

Muriel Boulakia | Zendy; Miguel Á. Fernández | Zendy; Jean-Frédéric Gerbeau | Zendy; Néjib Zemzemi | Zendy

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A Coupled System of PDEs and ODEs Arising in Electrocardiograms Modeling

Author(s) -

Muriel Boulakia,

Miguel Á. Fernández,

Jean-Frédéric Gerbeau,

Néjib Zemzemi

Publication year - 2008

Publication title -

applied mathematics research express

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.763

H-Index - 20

eISSN - 1687-1200

pISSN - 1687-1197

DOI - 10.1093/amrx/abn002

Subject(s) - uniqueness , degenerate energy levels , mathematics , compact space , partial differential equation , ode , regularization (linguistics) , mathematical analysis , computer science , physics , quantum mechanics , artificial intelligence

International audienceWe study the well-posedness of a coupled system of PDEs and ODEs arising in the numerical simulation of electrocardiograms. It consists of a system of degenerate reaction-diffusion equations, the so-called bidomain equations, governing the electrical activity of the heart, and a diffusion equation governing the potential in the surrounding tissues. Global existence of weak solutions is proved for an abstract class of ionic models including Mitchell-Schaeffer, FitzHugh-Nagumo, Aliev-Panfilov and MacCulloch. Uniqueness is proved in the case of the FitzHugh-Nagumo ionic model. The proof is based on a regularisation argument with a Faedo-Galerkin/compactness procedure

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