English

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}
}