On the asymptotic behaviour of anisotropic energies arising in the cardiac bidomain model
Luigi Ambrosio
Scuola Normale Superiore, Pisa, ItalyGiuseppe Savaré
Università di Pavia, ItalyPiero Colli Franzone
Università di Pavia, Italy
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Abstract
We study the -convergence of a family of vectorial integral functionals, which are the sum of a vanishing anisotropic quadratic form in the gradients and a penalizing double-well potential depending only on a linear combination of the components of their argument. This particular feature arises from the study of the so-called ‘bidomain model’ for the cardiac electric field; one of its consequences is that the -norm of a minimizing sequence can be unbounded and therefore a lack of coercivity occurs. We characterize the -limit as a surface integral functional, whose integrand is a convex function of the normal and can be computed by solving a localized minimization problem.
Cite this article
Luigi Ambrosio, Giuseppe Savaré, Piero Colli Franzone, On the asymptotic behaviour of anisotropic energies arising in the cardiac bidomain model. Interfaces Free Bound. 2 (2000), no. 3, pp. 213–266
DOI 10.4171/IFB/19