Motion by anisotropic mean curvature as sharp interface limit of an inhomogeneous and anisotropic Allen-Cahn equation

Details Motion by anisotropic mean curvature as sharp interface limit of an inhomogeneous and anisotropic Allen-Cahn equation Motion by anisotropic mean curvature as sharp interface limit of an inhomogeneous and anisotropic Allen-Cahn equation

2009-06-07

arxiv.org/abs/0906.1331v1

Mathematics

Analysis of PDEs

Scientific paper

We study the singular limit of a spatially inhomogeneous and anisotropic reaction-diffusion equation. We use a Finsler metric related to the anisotropic diffusion term and work in relative geometry. We prove a weak comparison principle and perform an analysis of both the generation and the motion of interfaces. The limit problem involves motion by anisotropic mean curvature. We also prove an optimal estimate of the thickness of the transition layer.

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