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Applied Mathematics Research eXpress (2008) Vol. 2008 : article ID abn002, 28 pages, doi:10.1093/amrx/abn002 published on April 1, 2008
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© The Author 2008. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org

A Coupled System of PDEs and ODEs Arising in Electrocardiograms Modeling

Muriel Boulakia1, Miguel Angel Fernández2, Jean-Frédéric Gerbeau2 and Nejib Zemzemi2,3

1 Université Paris 6, Laboratoire Jacques-Louis Lions, REO project-team, F-75005 Paris, France
2 INRIA, REO project-team, Rocquencourt, BP 105, F–78153 Le Chesnay Cedex, France
3 Université Paris 11, Laboratoire de mathématiques d'Orsay, Bâtiment 425, 91405 Orsay Cedex, France

Correspondence: Correspondence to be sent to: E-mail: jean-frederic.gerbeau{at}inria.fr

We 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 McCulloch. Uniqueness is proved in the case of the FitzHugh–Nagumo ionic model. The proof is based on a regularization argument with a Faedo–Galerkin/compactness procedure.


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