## Advances in Differential Equations

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

#### 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.

#### Article information

Source
Adv. Differential Equations, Volume 18, Number 9/10 (2013), 895-934.

Dates
First available in Project Euclid: 2 July 2013

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