Global Existence and Blow-up in Finite Time for a Class of Finitely Degenerate Semilinear Pseudo-parabolic Equations

被引：14

作者：

Chen, Hua ^{[1
]}

Xu, Hui Yang ^{[1
]}

机构：

[1] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Hubei, Peoples R China

来源：

ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2019年 / 35卷 / 07期

基金：

中国国家自然科学基金;

关键词：

Finitely degenerate pseudo-parabolic equation; global existence; blow-up; decay estimate; NONEXISTENCE; THEOREMS;

D O I：

10.1007/s10114-019-8037-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the initial-boundary value problem for the semilinear pseudo-parabolic equations u(t) - (X)u(t) - (X)u = |u|(p-1)u, where X = (X-1,X-2,...,X-m) is a system of real smooth vector fields which satisfy the Hormander's condition, and (X) = X=mml:mstyle displaystyle=true Sigma j=1mXj2 mml:mstyle is a finitely degenerate elliptic operator. By using potential well method, we first prove the invariance of some sets and vacuum isolating of solutions. Then, 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. The asymptotic behavior of the global solutions and a lower bound for blow-up time of local solution are also given.

引用

页码：1143 / 1162

页数：20