Volume 57, Issue 3
Global Existence of a Mean Curvature Flow in a Cone

Neng Ai, Bendong Lou, Jiashu Song, Pei Yang & Xin Zhang

J. Math. Study, 57 (2024), pp. 278-293.

Published online: 2024-10

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  • 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.

  • AMS Subject Headings

35K93, 53E10, 53A05, 35R35

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COPYRIGHT: © Global Science Press

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@Article{JMS-57-278, author = {Ai , NengLou , BendongSong , JiashuYang , Pei and Zhang , Xin}, title = {Global Existence of a Mean Curvature Flow in a Cone}, journal = {Journal of Mathematical Study}, year = {2024}, volume = {57}, number = {3}, pages = {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.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v57n3.24.03}, url = {http://global-sci.org/intro/article_detail/jms/23489.html} }
TY - JOUR T1 - Global Existence of a Mean Curvature Flow in a Cone AU - Ai , Neng AU - Lou , Bendong AU - Song , Jiashu AU - Yang , Pei AU - Zhang , Xin JO - Journal of Mathematical Study VL - 3 SP - 278 EP - 293 PY - 2024 DA - 2024/10 SN - 57 DO - http://doi.org/10.4208/jms.v57n3.24.03 UR - https://global-sci.org/intro/article_detail/jms/23489.html KW - Mean curvature flow, quasilinear parabolic equation, free boundary problem, self-similar solution. AB -

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.

Ai , NengLou , BendongSong , JiashuYang , Pei and Zhang , Xin. (2024). Global Existence of a Mean Curvature Flow in a Cone. Journal of Mathematical Study. 57 (3). 278-293. doi:10.4208/jms.v57n3.24.03
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