速度依赖于高斯曲率倒数的非参数曲面发展

刘辉昭;王光烈

数学学报 ›› 2002, Vol. 45 ›› Issue (1) : 43-58.

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PDF(547 KB)
数学学报 ›› 2002, Vol. 45 ›› Issue (1) : 43-58. DOI: 10.12386/A2002sxxb0007
论文

速度依赖于高斯曲率倒数的非参数曲面发展

    刘辉昭;王光烈
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Evolution of Nonparametric Surfaces with Speed Depending on the Reciprocal of the Gauss Curvature

    Hui Zhao LIU(1),Guang Lie WANG
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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 / 渐进性 / 存在唯一性

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刘辉昭;王光烈. 速度依赖于高斯曲率倒数的非参数曲面发展. 数学学报, 2002, 45(1): 43-58 https://doi.org/10.12386/A2002sxxb0007
Hui Zhao LIU(1),Guang Lie WANG. Evolution of Nonparametric Surfaces with Speed Depending on the Reciprocal of the Gauss Curvature. Acta Mathematica Sinica, Chinese Series, 2002, 45(1): 43-58 https://doi.org/10.12386/A2002sxxb0007
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