一类具强阻尼的Sine-Gordon型方程解的存在及惟一性

The Existence and Uniqueness of Solution for a Class Sine-Gordon Equations with Strong Damping

在Roger-Temam所提出的Sine-Gordon模型的基础上,考虑材料粘性效应、介质阻尼以及轴向载荷的作用,研究了更一般的一类广义非线性的具有强阻尼的Sine-Gordon型方程。对于所建立的方程我们应用Faedo-Galerkin方法,在相应的初边界条件下,证明了该方程局部解的存在性及唯一性。

In this paper,a generalized nonlinear strong damping Sine-Gordon equation is set up on the basis of Roger-Temam＇s Sine-Gordon model, simultaneously considering the viscous effect of material, strong damping and axial loads. By using Galerkin method, the existence and uniqueness of local solution for the initial boundary value problems are proved.