狄氏边条件无电容效应的Sine-Gordon系统的动力学

Dynamics of Sine-Gordon System Without Capacitance Effect Under Dirichlet Boundary Condition

证明无电容效应的Sine Gordon系数的全局吸引子的存在性 ,并指出当扩散系统适当大时全局吸引子即为系统的唯一周期解 .还证明系统在自治情形时是一个梯度系统 .

In this paper we prove the existence of global attractor for the Sine Gordon system without capaciance effect, pointing out the global attractor is the unique periodic solution of the system when the diffusion constant is sufficiently large. We also prove the autonomous system is a gradient system.