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 H^1 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.
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.
作者
吴国春
谭忠
许建开
Guochun WU;Zhong TAN;Jiankai XU
基金
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)
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)
