Existence of weak solution for mean curvature flow with transport term and forcing term

Keisuke Takasao

doi:10.3934/cpaa.2020116

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2020, Volume 19, Issue 5: 2655-2677. Doi: 10.3934/cpaa.2020116

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functions on open domains: the Wiener case and a Fomin differentiable case

Existence of weak solution for mean curvature flow with transport term and forcing term

Keisuke Takasao

Department of Mathematics/Hakubi Center, Kyoto University, Kitashirakawa-Oiwakecho Sakyo Kyoto 606-8502, Japan

Received: February 2019

Revised: October 2019

Published: March 2020

This work was supported by JSPS KAKENHI Grant Numbers JP16K17622, JP18H03670, and JSPS Leading Initiative for Excellent Young Researchers (LEADER) operated by Funds for the Development of Human Resources in Science and Technology

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Abstract

We study the mean curvature flow with given non-smooth transport term and forcing term, in suitable Sobolev spaces. We prove the global existence of the weak solutions for the mean curvature flow with the terms, by using the modified Allen-Cahn equation that holds useful properties such as the monotonicity formula.

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Mathematics Subject Classification: Primary: 35K93, Secondary: 53C44.

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