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速度依赖于高斯曲率倒数的非参数曲面发展
Evolution of Nonparametric Surfaces with Speed Depending on the Reciprocal of the Gauss Curvature
【摘要】 本文考虑具边值条件的曲面发展问题.与以往的问题不同(见[1-4]),这里讨论是的曲面发展速度与曲面曲率成反比的情况.本文得到了描述这种曲面发展的非线性非一致抛物方程第一初边值问题解的存在性、唯一性和渐进性.
【Abstract】 We consider an curvature flows with boundary condition. In contradiction to the former works [1-4] and others,here the speed of flow of surfaces is in inversely proportional to curvature of surface. We show that the corresponding first initial-boundary problem admits a classical convex solution for all time and then investigate asymptotic behaviour of the solution.
【关键词】 曲面发展;
Gaussian曲率;
第一初边值问题;
存在唯一性;
渐进性;
【Key words】 Flow of surfaces; Gauss curvature; First initial-boundary problem; Classical convex solution; Asymptotic behaviour;
【Key words】 Flow of surfaces; Gauss curvature; First initial-boundary problem; Classical convex solution; Asymptotic behaviour;
【基金】 国家自然科学基金资助项目;博士点基金资助项目
- 【文献出处】 数学学报 ,Acta Mathematica Sinica , 编辑部邮箱 ,2002年01期
- 【分类号】O175.26;O175.29
- 【被引频次】1
- 【下载频次】68