Calculus of Variations and Geometric Measure Theory

S. Amato - G. Bellettini - M. Paolini

The nonlinear multidomain model: a new formal asymptotic analysis

created by amato on 31 Jan 2013


Submitted Paper

Inserted: 31 jan 2013
Last Updated: 31 jan 2013

Year: 2013


We study the asymptotic analysis of a singularly perturbed weakly parabolic system of $m$- equations of anisotropic reaction-diffusion type. Our main result formally shows that solutions to the system approximate a geometric motion of a hypersurface by anisotropic mean curvature. The anisotropy, supposed to be uniformly convex, is explicit and turns out to be the dual of the star-shaped combination of the m original anisotropies.

Keywords: reaction-diffusion systems, nonconvex anisotropy, anisotropic mean curvature flow