TY - UNPB

T1 - Nonconvex mean curvature flow as a formal singular limit of the nonlinear bidomain model

AU - Paolini, Maurizio

AU - Pasquarelli, Franco

AU - Bellettini, Giovanni

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

KW - electrocardiology

KW - illposed problems

KW - reaction-diffusion systems

KW - electrocardiology

KW - illposed problems

KW - reaction-diffusion systems

UR - http://hdl.handle.net/10807/31199

M3 - Working paper

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

ER -