中国科学技术大学学报 ›› 2021, Vol. 51 ›› Issue (6): 447-452.DOI: 10.52396/JUST-2021-0076

• 研究论文:数学 • 上一篇    下一篇

一个带锥曲面上的四阶线性抛物方程

张方旭*   

  1. 中国科学技术大学数学科学学院, 安徽合肥 230026
  • 收稿日期:2021-03-17 修回日期:2021-06-10 出版日期:2021-06-30 发布日期:2021-12-06
  • 通讯作者: * E-mail:fxzhang@mail.ustc.edu.cn

A fourth order linear parabolic equation on conical surfaces

Zhang Fangxu   

  1. School of Mathematical Sciences, University of Science and Technology of China, Heifei 230026, China
  • Received:2021-03-17 Revised:2021-06-10 Online:2021-06-30 Published:2021-12-06
  • Contact: * E-mail: fxzhang@mail.ustc.edu.cn

摘要: 考虑一个带锥曲面上的四阶线性抛物方程,利用能量分析和逼近的方法,证明了方程在一个具有逼近性质的空间上的解的存在唯一性.最后,证明了当β∈(-1,0)时,对于一类函数这个性质等价于能量有限.

关键词: 抛物方程, Calabi流, 锥奇点

Abstract: A parabolic equation of fourth order on surfaces with conical singularities is considered. By the analysis of energy and approximations, the existence and uniqueness of the solution of this equation in a special space that has some approximation property are proved. Finally, it's proved that the property is equivalent to the finiteness of energy for some functions when β∈(-1,0).

Key words: parabolic equation, Calabi flow, conical singularity

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