中文摘要：

同时考虑黏性效应及外阻尼作用研究了一类广义强阻尼Sine-Gordon方程．利用Galerkin方法，首先证明了该方程在初值u（x，0）∈H0^1（Ω），u。（x，0）∈L^2（Ω）的条件下初边值问题存在整体弱解u（x，t），并证明了整体弱解关于初始条件具有连续的依赖性及唯一性．其次，证明了该方程在初值u（x，0）∈H0^1（Ω）∩H^2（Ω），u。（x，0）∈H0^1（Ω）的条件下初边值问题存在整体强解u（x，t）．

英文摘要：

A kind of generalized Sine-Gordon equations with strong damping are studied, considering both viscosity effect and external damping. Firstly, by the aid of Galerkin method, under the initial value conditions u（x,0）∈H0^1（Ω）,u.（x,0）∈L^2（Ω）, we prove the existence and uniqueness of a global weak solution u （x, t ） for the initial boundary value problems and the constant dependence of solution on the initial value. Secondly, under the initial value conditionsu（x,0）∈H0^1（Ω）∩H^2（Ω）,u.（x,0）∈H0^1（Ω）, the course of proof of the existence of strong solution u （ x, t ） is also explained by using Galerkin method.