期刊论文

Tan, Zhong

英文

数学物理学报(英文版)

0252-9602

2019

39

5

1397-1405

10.1007/s10473-019-0516-8

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).

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We study the heat flow of equation of H-surface with non-zero Dirichlet boundary in the present article. Introducing the “stable set” $$\mathfrak{M}_2$$ and “unstable set” $$\mathfrak{M}_1$$ , we show that there exists a unique global solution provided the initial data belong to $$\mathfrak{M}_2$$ 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 belo...