一类具有强阻尼和强时滞的粘弹性方程解的存在性

Global Existence of the Solution to A Class of Viscoelastic Wave Equation with Strong Damping and Strong Delay

研究一类具有强阻尼和强时滞作用的粘弹性波动方程|u_t|~ρu_(tt)-Δu-Δu_(tt)+∫_0~tg(t-s)Δu(s)ds-μ_1Δu_t-μ_2Δu_t(t-τ)=0的初边值问题,当μ_1、μ_2和记忆核g满足一定条件时,利用Faedo-Galerkin方法证明了解的整体存在性.

In this paper,we consider a class of viscoelastic wave equation with strong damping and strong delay｜ut｜~ρu（tt）-Δu-Δu（tt）＋∫0~tg（t-s）Δu（s）ds-μ1Δut-μ2Δut（t-τ）=0 in a bounded domain.By using Faedo-Galerkin method,we obtain the global existence of the solution to the problem under suitable conditions onμ1,μ2 and the memory kernel g.