Global Existence of a Mean Curvature Flow in a Cone
Year: 2024
Author: Neng Ai, Bendong Lou, Jiashu Song, Pei Yang, Xin Zhang
Journal of Mathematical Study, Vol. 57 (2024), Iss. 3 : pp. 278–293
Abstract
We consider a mean curvature flow in a cone, that is, a hypersurface in a cone which propagates toward the opening of the cone with normal velocity depending on its mean curvature. In addition, the contact angle between the hypersurface and the cone boundary depending on its position. First, we construct a family of radially symmetric self-similar solutions. Then we use these solutions to give a priori estimates for the solutions of the initial boundary value problems, and show their global existence.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v57n3.24.03
Journal of Mathematical Study, Vol. 57 (2024), Iss. 3 : pp. 278–293
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Mean curvature flow quasilinear parabolic equation free boundary problem self-similar solution.
Author Details
Neng Ai Email
Bendong Lou Email
Jiashu Song Email
Pei Yang Email
Xin Zhang Email