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.
Guochun WU
,
Zhong TAN
,
Jiankai XU
. ON THE HEAT FLOW OF EQUATION OF H-SURFACE[J]. Acta mathematica scientia, Series B, 2019
, 39(5)
: 1397
-1405
.
DOI: 10.1007/s10473-019-0516-8
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