Global existence, asymptotic stability and blow-up of solutions for the generalized Boussinesq equation with nonlinear boundary condition
Global existence, asymptotic stability and blow-up of solutions for the generalized Boussinesq equation with nonlinear boundary condition
复制标题
具有非线性边界条件的广义Boussinesq方程的全局存在性、渐近稳定性和解的爆炸
DOI：
10.1002/mana.201700350
复制
发表时间：
2020
影响因子：
1
通讯作者：
Liu Gongwei
中科院分区：
文献类型：
--
作者：
Zhang Hongwei;Hu Qingying;Liu Gongwei
本文研究了一类具有非线性内源和边界吸收项的广义Boussinesq方程的初边值问题。首先利用标准Galerkin方法证明了解的局部存在性。然后我们证明了解的整体存在性和能量函数在初始数据的某些限制下的一般衰减性。我们还证明了一个blow-up的结果，分别为正和负的初始能量的解决方案。
In this paper, we consider initial boundary value problem of the generalized Boussinesq equation with nonlinear interior source and boundary absorptive terms. We establish firstly the local existence of solutions by standard Galerkin method. Then we prove both the global existence of the solution and a general decay of the energy functions under some restrictions on the initial data. We also prove a blow‐up result for solutions with positive and negative initial energy respectively.