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] Mathematics and Science College, Shanghai Normal University, Shanghai, 200234, China; [2] Department of Mathematics, East China University of Science and Technology, Shanghai, 200237, China

年份：2020

外文期刊名：arXiv

收录：EI(收录号：20200423070)

语种：英文

摘要：We consider an anisotropic curvature flow V = A(n)H +B(n) in a band domain Ω:= [?1, 1]× R, where n, V and H denote the unit normal vector, normal velocity and curvature, respectively, of a graphic curve Γt. We consider the case when A > 0 > B and the curve Γt contacts ?±Ω with slopes equaling to ±1 times of its height (which are unbounded when the solution moves to infinity). First, we present the global well-posedness and then, under some symmetric assumptions on A and B, we show the uniform interior gradient estimates for the solution. Based on these estimates, we prove that Γt converges as t → ∞ in Cloc2,1((?1, 1) × R) topology to a cup-like traveling wave with infinite derivatives on the boundaries. Copyright ? 2020, The Authors. All rights reserved.