色噪声驱动的非自治非经典扩散方程的拉回随机吸引子

Pullback random attractors of non-autonomous non-classical diffusion equations driven by colored noise

本文研究无界区域上带色噪声的非自治非经典扩散方程解的渐近性.为了克服Sobolev嵌入在无界区域上的非紧性,利用Ball能量方程的思想,本文证明与问题相关的多值随机动力系统在H^(1)(R^(n))中拉回随机吸引子的存在性.

In this paper,we study the asymptotic behavior of solutions of non-autonomous non-classical diffusion equations driven by colored noise defined on unbounded domains.To overcome the non-compactness of Sobolev embeddings on unbounded domains,using the idea of Ball energy equation,we prove the existence of pullback random attractor in H^(1)(R^(n))for the multi-value random dynamical system associated with the problem.