GLOBAL EXISTENCE,EXPONENTIAL DECAY AND BLOW-UP IN FINITE TIME FOR A CLASS OF FINITELY DEGENERATE SEMILINEAR PARABOLIC EQUATIONS

被引：0

作者：

陈化 ^{[1
,2
]}

徐辉阳 ^{[1
,2
]}

机构：

[1] School of Mathematics and Statistics,Wuhan University

[2] Computational Science Hubei Key Laboratory,Wuhan University

来源：

ActaMathematicaScientia | 2019年 / 39卷 / 05期

关键词：

finitely degenerate parabolic equation; global existence; blow-up; decay estimate;

D O I：

暂无

中图分类号：

O175.26 [抛物型方程];

学科分类号：

070104 ;

摘要：

In this paper,we study the initial-boundary value problem for the semilinear parabolic equations u_t-△Xu=|u|p-1u,where X=（X1,X2,…,Xm） is a system of real smooth vector fields which satisfy the H?rmander's condition,and △X=∑j=1m Xj2 is a finitely degenerate elliptic operator.Using potential well method,we first prove the invariance of some sets and vacuum isolating of solutions.Finally,by the Galerkin method and the concavity method we show the global existence and blow-up in finite time of solutions with low initial energy or critical initial energy,and also we discuss the asymptotic behavior of the global solutions.

引用

页码：1290 / 1308

页数：19

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