文献类型：期刊文献

英文题名：ON A CURVATURE FLOW IN A BAND DOMAIN WITH UNBOUNDED BOUNDARY SLOPES

作者：Yuan, Lixia[1];Zhao, Wei[2]

机构：[1]Shanghai Normal Univ, Math & Sci Coll, Shanghai 200234, Peoples R China;[2]East China Univ Sci & Technol, Sch Math, Shanghai 200237, Peoples R China

年份：2022

卷号：42

期号：1

起止页码：261

外文期刊名：DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000697778700001)】；

基金：The first author is supported by by NNSFC (No. 12001375) . The second author is supported NNSFC (No. 11761058) and NSFS (No. 19ZR1411700, No. 21ZR1418300) .

语种：英文

外文关键词：Anisotropic curvature flow; cup-like; traveling wave; asymptotic behavior

摘要：This paper is devoted to an anisotropic curvature flow of the form V = A(n)H + B(n) in a band domain Omega := [1, 1] x R, where n, V and H denote respectively the unit normal vector, normal velocity and curvature of a graphic curve Gamma(t). We require that the curve Gamma(t) contacts partial derivative Omega with slopes equaling to the heights of the contact points (which corresponds to a kind of Robin boundary conditions). In spite of the unboundedness of the boundary slopes, we are able to obtain the uniform interior gradient estimates for the solutions by using the zero number argument. Furthermore, when t -> infinity, we show that Gamma(t) converges to a traveling wave with cup-shaped profile and infinite boundary slopes in the C-loc(2,1)((-1, 1) x R)-topology.