一类广义强阻尼Sine-Gordon方程的整体解

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)∈H¹₀(Ω)，u_t(x，0)∈L²(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 关键词： Sine-Gordon型方程 强阻尼 Galerkin方法 整体解

Global solutions for a kind of generalized Sine-Gordon equation with strong damping

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，t)∈H¹₀ (Ω) ，u_t∈L₂ (Ω)，we prove the existence and uniqueness of a global weak solution u(x，t) for the initial boundary value problems and the constant dependenceof solution on the initial value- Secondly， under the initial value conditionsu(x，0)∈H¹₀ (Ω)∩H²(Ω)，u_t(x，0)∈H¹₀ (Ω)，the course of proof of the existence of strong solution u(x，t) is also explained by using Galerkin method-