材料中含记忆项的非自治分数阶随机热方程的渐近行为

Asymptotic Behavior of Non-autonomous Fractional Stochastic Heat Equations in Materials with Memory

研究材料中带记忆项的非自治分数阶随机反应扩散方程的渐近行为.证明随机吸引子的存在性和随机吸引子在噪声强度ε→0时的上半连续性.由于记忆项包含现象过去的全部历史,不能证明方程生成的随机动力系统的紧性,但是可以通过分解方法证明其渐近紧性.

In this paper,we investigate the asymptotic behavior of non-autonomous fractional stochastic reaction-diffusion equations in materials with memory.We prove the existence of random attractors and the upper semi-continuity of random attractors when the intensity of noise approaches zero.Due to the fact that the memory term includes the whole past history of the phenomenon,the compactness of the generated RDS can not be proved while its asymptotic compactness can be proved by the splitting method.