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

作　　者：Hua CHEN Huiyang XU 陈化;徐辉阳(School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China Computational Science Hubei Key Laboratory, Wuhan University, Wuhan 430072, China)

机构地区：[1]School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China Computational Science Hubei Key Laboratory, Wuhan University, Wuhan 430072, China

出　　处：《Acta Mathematica Scientia》2019年第5期1290-1308,共19页数学物理学报（B辑英文版）

基　　金：supported by National Natural Science Foundation of China(11631011 and 11626251)

摘　　要：In this paper,we study the initial-boundary value problem for the semilinear parabolic equations ut-△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.In this paper, we study the initial-boundary value problem for the semilinear parabolic equations ut -△Xu=|u|^p-1u, where X=(X1, X2,…, Xm) is a system of real smooth vector fields which satisfy the Hormander's condition, and △x=m∑j=1Xj^2is 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.

关 键 词：finitely DEGENERATE PARABOLIC equation global EXISTENCE BLOW-UP DECAY estimate 

分 类 号：O[理学]