Boussinesq方程弱解的存在性和真空孤立现象（英文）

Existence and Vacuum Isolating Phenomenon of the Weak Solutions for the Boussinesq Equation

本文研究一类具有双阻尼非线性六阶Boussinesq方程的初边值问题,结合先验估计,利用Galerkin方法及紧性定理,得到该方程弱解的存在性.进一步,借助势井族的定义得到解的真空孤立现象,这是关于此方程的第一个结论.

The initial boundary value problem for a kind of nonlinear sixth-order double-damping Boussinesq equation is considered. Firstly, the existence of the weak solutions to the problem is established by a priori estimates, Galerkin method and the compactness theorem. Moreover, by introducing a family of potential wells, we prove the vacuum isolating phenomenon of solutions, which is the first result for this equation.