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

作     者：Xiao SU Shubin WANG 苏晓;王书彬

作者机构：College of ScienceHenan University of TechnologyZhengzhou450001China School of Mathematics and StatisticsZhengzhou UniversityZhengzhou450001China 

出 版 物：《Acta Mathematica Scientia》 (数学物理学报（B辑英文版）)

年 卷 期：2024年第44卷第5期

页      面：1766-1786页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

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) 

主　　题：damped Boussinesq equation Cauchy problem global solutions blow-up 

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 *** the help of linear time-space estimates,we establish the local existence and uniqueness of solutions by means of the contraction mapping *** global existence and blow-up of the solutions at both subcritical and critical initial energy levels are ***,we construct the sufficient conditions of finite time blow-up of the solutions with arbitrary positive initial energy.