Remarks on large time behavior of level-set mean curvature flow equations with driving and source terms

Yoshikazu Giga; Hiroyoshi Mitake; Hung V. Tran

doi:10.3934/dcdsb.2019228

Article Contents

2020, Volume 25, Issue 10: 3983-3999. Doi: 10.3934/dcdsb.2019228

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Remarks on large time behavior of level-set mean curvature flow equations with driving and source terms

1.
Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153-8914, Japan
2.
Department of Mathematics, University of Wisconsin Madison, Van Vleck Hall, 480 Lincoln Drive, Madison, Wisconsin 53706, USA

^* Corresponding author: Yoshikazu Giga
^* Corresponding author: Yoshikazu Giga

Received: May 31, 2019

Revised: May 31, 2019

Early access: September 2019

Published: October 2020

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Abstract

We study a level-set mean curvature flow equation with driving and source terms, and establish convergence results on the asymptotic behavior of solutions as time goes to infinity under some additional assumptions. We also study the associated stationary problem in details in a particular case, and establish Alexandrov's theorem in two dimensions in the viscosity sense, which is of independent interest.

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Mathematics Subject Classification: Primary: 35B40; Secondary: 35K93, 35K20.

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