Nonconvex mean curvature flow as a formal singular limit of the nonlinear bidomain model

Maurizio Paolini, Franco Pasquarelli, Giovanni Bellettini

Risultato della ricerca: Working paper

Abstract

In this paper we study the nonconvex anisotropic mean curvature flow of a hypersurface. This corresponds to an anisotropic mean curvature flow where the anisotropy has a nonconvex Frank diagram. The geometric evolution law is therefore forward-backward parabolic in character, hence ill-posed in general. We study a particular regularization of this geometric evolution, obtained with a nonlinear version of the so-called bidomain model. This is described by a degenerate system of two uniformly parabolic equations of reaction-diffusion type, scaled with a positive parameter $\epsilon$. We analyze some properties of the formal limit of solutions of this system as $\epsilon \to 0$, and show its connection with nonconvex mean curvature flow. Several numerical experiments substantiating the formal asymptotic analysis are presented.
Lingua originaleEnglish
Numero di pagine35
Stato di pubblicazionePubblicato - 2012

Keywords

  • electrocardiology
  • illposed problems
  • reaction-diffusion systems

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