波方程与欧拉伯努利板方程耦合系统的全局吸引子

Global Attractor for a Coupled System of Wave and Euler-Bernoulli Plate Equation with Boundary Weak Damping

该文研究了黎曼流形上半线性波方程与欧拉伯努利板方程耦合系统的长时间性态,该系统具有边界耗散结构.在逃逸向量场存在性假设下利用乘子方法证明了原耦合系统全局紧吸引子的存在性,该存在性与黎曼度量的曲率性质有关.

In this paper,we consider the longtime behavior for a coupled system consisting of the semi-linear wave equation with nonlinear boundary dissipation and the Euler-Bernoulli plate equation on a Riemannian manifold.It is shown that the existence of global and compact attractors depends on the curvature properties of the metric on the manifold by using the multiplier method and the hypothesis of escape vector field.