ON THE HEAT FLOW OF EQUATION OF H-SURFACE  

作　　者：Guochun WU Zhong TAN Jiankai XU 吴国春;谭忠;许建开(Fujian Province University Key Laboratory of Computational Science, School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China;School of Mathematical Sciences and Fujian Provincial Key Laboratory on Mathematical Modeling and Scientific Computing, Xiamen University, Xiamen 361005, China;College of Information Science and Technology, Hunan Agriculture University, Changsha 410128, China)

机构地区：[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

出　　处：《Acta Mathematica Scientia》2019年第5期1397-1405,共9页数学物理学报（B辑英文版）

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)

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.

关 键 词：H-surface non-zero DIRICHLET BOUNDARY SINGULARITY global solutions 

分 类 号：O[理学]