Generation, motion and thickness of transition layers for a nonlocal Allen-Cahn equation
Analysis of PDEs
2009-06-09 v1
Abstract
We investigate the behavior, as a small parameter tends to zero, of a nonlocal Allen-Cahn equation. Given a rather general initial data, we perform a rigorous analysis of both the generation and the motion of interface, and obtain a new estimate for its thickness. The limit problem involves motion by mean curvature together with a nonlocal effect (which allows the possibility of nontrivial stationary state).
Keywords
Cite
@article{arxiv.0906.1330,
title = {Generation, motion and thickness of transition layers for a nonlocal Allen-Cahn equation},
author = {Matthieu Alfaro},
journal= {arXiv preprint arXiv:0906.1330},
year = {2009}
}