Calculus of Variations and Geometric Measure Theory

A. Cesaroni - C. Muratov - M. Novaga

Asymptotic behavior of attractors for inhomogeneous Allen-Cahn equations

created by novaga on 20 Feb 2014
modified on 03 May 2015


Published Paper

Inserted: 20 feb 2014
Last Updated: 3 may 2015

Journal: RIMS Kokyuroku
Volume: 1924
Pages: 97-114
Year: 2014

Submitted to


We consider front propagation problems for forced mean curvature flows with a transport term and their phase field variants that take place in stratified media, i.e., heterogeneous media whose characteristics do not vary in one direction. We provide a convergence result relating asymptotic in time front propagation in the diffuse interface case to that in the sharp interface case, for suitably balanced nonlinearities of Allen-Cahn type. Our results generalize previous results for forced Allen-Cahn equations.