Attractors of Stochastic Wave Equations With Nonlinear-Damping and Dynamic Boundary Conditions
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摘要: 研究了一类动态边界上的随机波动方程.通过建立一种分解技术,证明了方程随机吸引子的存在性.分解同时表明,该吸引子上的点(或者解)一定满足某种稳定的边界条件.最后,证明了吸引子的结构与分解所得的静态边界上波动方程的随机吸引子相同.Abstract: A class of wave equations with dynamic boundary conditions were studied. Through suitable decomposition, the existence of the stochastic attractor was proved. The decomposition shows that the point (or solution) of the attractor satisfies some stationary boundary condition. Finally, the attractor also exists in the stochastic dynamic system determined by the stochastic wave equation with the static boundary condition developed in decomposition.
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Key words:
- dynamic boundary condition /
- wave equation /
- stochastic attractor
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