数学物理学报(英文版) ›› 2019, Vol. 39 ›› Issue (5): 1397-1405.doi: 10.1007/s10473-019-0516-8

• 论文 • 上一篇    下一篇

ON THE HEAT FLOW OF EQUATION OF H-SURFACE

吴国春1, 谭忠2, 许建开3   

  1. 1. Fujian Province University Key Laboratory of Computational Science, School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China;
    2. School of Mathematical Sciences and Fujian Provincial Key Laboratory on Mathematical Modeling and Scientific Computing, Xiamen University, Xiamen 361005, China;
    3. College of Information Science and Technology, Hunan Agriculture University, Changsha 410128, China
  • 收稿日期:2017-09-25 修回日期:2019-03-04 出版日期:2019-10-25 发布日期:2019-11-11
  • 通讯作者: Zhong TAN E-mail:ztan85@163.com
  • 作者简介:Guochun WU,E-mail:guochunwu@126.com;Jiankai XU,E-mail:jiankaixu@126.com
  • 基金资助:
    Guochun Wu's research was in part supported by National Natural Science Foundation of China (11701193, 11671086), Natural Science Foundation of Fujian Province (2018J05005), Program for Innovative Research Team in Science and Technology in Fujian Province University Quanzhou High-Level Talents Support Plan (2017ZT012). Zhong Tan's research was in part supported by National Natural Science Foundation of China (11271305, 11531010). Jiankai Xu's research was in part supported by National Natural Science Foundation (11671086, 11871208), Natural Science Foundation of Hunan Province (2018JJ2159).

ON THE HEAT FLOW OF EQUATION OF H-SURFACE

Guochun WU1, Zhong TAN2, Jiankai XU3   

  1. 1. Fujian Province University Key Laboratory of Computational Science, School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China;
    2. School of Mathematical Sciences and Fujian Provincial Key Laboratory on Mathematical Modeling and Scientific Computing, Xiamen University, Xiamen 361005, China;
    3. College of Information Science and Technology, Hunan Agriculture University, Changsha 410128, China
  • Received:2017-09-25 Revised:2019-03-04 Online:2019-10-25 Published:2019-11-11
  • Contact: Zhong TAN E-mail:ztan85@163.com
  • Supported by:
    Guochun Wu's research was in part supported by National Natural Science Foundation of China (11701193, 11671086), Natural Science Foundation of Fujian Province (2018J05005), Program for Innovative Research Team in Science and Technology in Fujian Province University Quanzhou High-Level Talents Support Plan (2017ZT012). Zhong Tan's research was in part supported by National Natural Science Foundation of China (11271305, 11531010). Jiankai Xu's research was in part supported by National Natural Science Foundation (11671086, 11871208), Natural Science Foundation of Hunan Province (2018JJ2159).

摘要: We study the heat flow of equation of H-surface with non-zero Dirichlet boundary in the present article. Introducing the "stable set" M2 and "unstable set" M1, we show that there exists a unique global solution provided the initial data belong to M2 and the global solution converges to zero in H1 exponentially as time goes to infinity. Moreover, we also prove that the local regular solution must blow up at finite time provided the initial data belong to M1.

关键词: H-surface, non-zero Dirichlet boundary, singularity, global solutions

Abstract: We study the heat flow of equation of H-surface with non-zero Dirichlet boundary in the present article. Introducing the "stable set" M2 and "unstable set" M1, we show that there exists a unique global solution provided the initial data belong to M2 and the global solution converges to zero in H1 exponentially as time goes to infinity. Moreover, we also prove that the local regular solution must blow up at finite time provided the initial data belong to M1.

Key words: H-surface, non-zero Dirichlet boundary, singularity, global solutions

中图分类号: 

  • 35J20