一类具有非线性强阻尼的粘弹性杆方程解的长时间动力学行为

Long Time Dynamic Behavior for a Class of Viscoelastic Rod Equations with Nonlinear Strong Damping

本文研究一类具有记忆项和非线性强阻尼项的波动方程.利用Faedo-Galerkin逼近方法, Lions-Aubin紧性定理证明了该问题整体弱解的存在唯一性;然后,利用常用的不等式证明了系统有界吸收集的存在性,通过验证半群的紧性得到系统整体吸引子的存在性.

This paper we considered the wave equation with memory and nonlinear strong damping.The existence and uniqueness of the global weak solution is proved by using the Faedo-Galerkin approximation method and the Lions-Aubin compactness theorem.Then,the existence of the bounded absorbing set of the semigroup is proved by some inequalities,and the existence of the global attractor of the system is obtained by proving the compactness of the semigroup.