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arXiv · 0906.1330

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

Matthieu Alfaro
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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).

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Matthieu Alfaro. 2009-06-07. Generation, motion and thickness of transition layers for a nonlocal Allen-Cahn equation. https://arxiv.org/abs/0906.1330

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