Translator Disclaimer
September/October 2013 Nonconvex mean curvature flow as a formal singular limit of the nonlinear bidomain model
Giovanni Bellettini, Maurizio Paolini, Franco Pasquarelli
Adv. Differential Equations 18(9/10): 895-934 (September/October 2013).

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.

Citation

Download Citation

Giovanni Bellettini. Maurizio Paolini. Franco Pasquarelli. "Nonconvex mean curvature flow as a formal singular limit of the nonlinear bidomain model." Adv. Differential Equations 18 (9/10) 895 - 934, September/October 2013.

Information

Published: September/October 2013
First available in Project Euclid: 2 July 2013

zbMATH: 1272.53054
MathSciNet: MR3100055

Subjects:
Primary: 35K40 , 47J06 , 53C44

Rights: Copyright © 2013 Khayyam Publishing, Inc.

JOURNAL ARTICLE
40 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.18 • No. 9/10 • September/October 2013
Back to Top