Generation, motion and thickness of transition layers for a nonlocal Allen-Cahn equation

Details Generation, motion and thickness of transition layers for a nonlocal Allen-Cahn equation Generation, motion and thickness of transition layers for a nonlocal Allen-Cahn equation

2009-06-07

arxiv.org/abs/0906.1330v1

Mathematics

Analysis of PDEs

Scientific paper

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).

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