非线性阻尼波方程在R3上的时间依赖吸引子

Time-Dependent Attractor of Nonlinear Damping Wave Equation on R3

基于时间依赖空间中的吸引子理论,本文研究了无界域上带有非线性阻尼的波方程解的长时间行 为。 利用压缩函数方法和一些估计技巧证明了过程的渐近紧性,进而得到了时间依赖吸引子的存在性。

Based on the attractor theory in time-dependent spaces, we consider long-time be- havior of solutions for the wave equation with nonlinear damping on the unbounded domain. We prove the asymptotic compactness of the process by using the contrative functions and some detailed estimates, thus the existence of time-dependent attractors is proved.