Linking anisotropic sharp and diffuse surface motion laws via gradient flows.

*(English)*Zbl 0844.35044The authors consider four laws of motion for sharp surfaces (e.g., motion by mean curvature or by the negative Laplacian of the mean curvature) and show that they can all be interpreted as gradient flows of the same energy functional corresponding to different choices of inner product. Anisotropic as well as isotropic energies are considered. They also obtain analogous results for the diffuse interface counterparts of these equations (e.g., Allen-Cahn and Cahn-Hilliard equations). For both classes of examples the anisotropy of the kinetics is incorporated into the inner product, not into the energy functional.

Reviewer: J.Urbas (Bonn)

##### MSC:

35K55 | Nonlinear parabolic equations |

82C24 | Interface problems; diffusion-limited aggregation in time-dependent statistical mechanics |

##### Keywords:

Allen-Cahn equation; diffuse interfaces; anisotropy; motion for sharp surfaces; motion by mean curvature; Cahn-Hilliard equations
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\textit{J. E. Taylor} and \textit{J. W. Cahn}, J. Stat. Phys. 77, No. 1--2, 183--197 (1994; Zbl 0844.35044)

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##### References:

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