ON THE CAUCHY PROBLEM FOR THE GENERALIZED BOUSSINESQ EQUATION WITH A DAMPED TERM  

作　　者：Xiao SU Shubin WANG 苏晓;王书彬(College of Science,Henan University of Technology,Zhengzhou,450001,China;School of Mathematics and Statistics,Zhengzhou University,Zhengzhou,450001,China)

机构地区：[1]College of Science,Henan University of Technology,Zhengzhou,450001,China [2]School of Mathematics and Statistics,Zhengzhou University,Zhengzhou,450001,China

出　　处：《Acta Mathematica Scientia》2024年第5期1766-1786,共21页数学物理学报（B辑英文版）

基　　金：supported by the National Natural Science Foundation of China(12301272);the Natural Science Foundation of Henan(202300410109);the Cultivation Programme for Young Backbone Teachers in Henan University of Technology,and the Innovative Funds Plan of Henan University of Technology(2020ZKCJ09).

摘　　要：This paper is devoted to the Cauchy problem for the generalized damped Boussinesq equation with a nonlinear source term in the natural energy space.With the help of linear time-space estimates,we establish the local existence and uniqueness of solutions by means of the contraction mapping principle.The global existence and blow-up of the solutions at both subcritical and critical initial energy levels are obtained.Moreover,we construct the sufficient conditions of finite time blow-up of the solutions with arbitrary positive initial energy.

关 键 词：damped Boussinesq equation Cauchy problem global solutions BLOW-UP 

分 类 号：O175[理学—数学]