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

Maurizio Paolini, Giovanni Bellettini, Franco Pasquarelli

Risultato della ricerca: Contributo in rivistaArticolo in rivistapeer review

3 Citazioni (Scopus)

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 ϵ. We analyze some properties of the formal limit of solutions of this system as ϵ→0+, and show its connection with nonconvex mean curvature flow. Several numerical experiments substantiating the formal asymptotic analysis are presented.
Lingua originaleEnglish
pagine (da-a)895-934
Numero di pagine40
RivistaAdvances in Differential Equations
Volume18
Stato di pubblicazionePubblicato - 2013

Keywords

  • bidomain model
  • nonconvex mean curvature flow

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