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 gl...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.展开更多
基金supported by National Natural Science Foundation of China(11701193,11671086)Natural Science Foundation of Fujian Province(2018J05005)+3 种基金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)
文摘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.
基金supported by the National Natural Science Foundation of China(No.12171314)the Innovation Program of Shanghai Municipal Education Commission(No.2021-01-07-00-02-E00087)。
文摘The authors investigate H-surfaces into static Lorentzian manifolds and show the Holder continuity of weak solutions.
