材料中带有记忆项的随机热方程在薄域上的随机吸引子

Random Attractors of Stochastic Heat Equations in Materials with Memory on Thin Domains

研究加性噪声驱动的随机积分微分方程在薄域上的动力学行为.证明在n+1维薄域上随机吸引子的存在性和唯一性.由于记忆项包含现象过去的全部历史,不能证明其随机动力系统的紧性,但是可以使用分解方法证明渐近紧性.

This paper deals with the dynamical behavior of a stochastic integro-differential equation driven by additive noise defined on thin domains.We prove the existence and uniqueness of random attractors for the equation in an(n+1)-dimensional thin domain.Due to the fact that the memory term includes the whole past history of the phenomenon,we are not able to prove the compactness of the generated RDS,but its asymptotic compactness can be proved by the splitting method.