具有双重阻尼的Boussineq方程解的存在性和渐近性

Existence and Asymptotic Behavior of Solution for the Generalized Boussinesq Equation with Double Damping

主要研究一类具有双重阻尼的六阶Boussineq方程的Cauchy问题,首先利用压缩映射原理推出局部解的适定性,并通过建立局部解的先验估计得到了整体解的存在性,最后利用乘子法证明解的渐近性.

This paper considers the existence and asymptotic behavior of solution for the Cauchy problem of the sixth order Boussineq equation with double damping.We deduce the well-posedness of the local solution by the contraction mapping principle,and obtain the existence of the global solution by establishing the prior estimate of the local solution.Finally,the asymptotic behavior of the solution is proved with the multiplier method.