随机非经典扩散方程的Wong-Zakai逼近  

Wong-Zakai Approximations_of Stochastic Nonclassical Diffusion Equation

作　　者：徐冬梅 俞智慧[1] 李富智 XU Dong-mei;YU Zhi-hui;LI Fu-zhi(School of Mathematics and Computer Science,Shangrao Normal University,Shangrao 334001,China)

机构地区：[1]上饶师范学院数学与计算机科学学院,江西上饶334001

出　　处：《数学的实践与认识》2023年第7期189-196,共8页Mathematics in Practice and Theory

基　　金：国家自然科学基金(12201415);江西省教育厅科学技术项目(GJJ211705);上饶师范学院校级教改课题(JG-21-23)。

摘　　要：研究了非自治随机非经典扩散方程的Wong-Zakai逼近在有界域上的动力学行为.方程中的两个非线性项在一定的假设下得到了方程解的一致估计,并利用正交谱分解的方法证明了方程的解在H_(0)^(1)(O)空间中的渐近紧性,由此证明了在Wong-Z akai逼近下该方程生成的非自治随机动力系统存在唯一的随机拉回吸引子.This paper studies the dynamics of the Wong-Zakai approximations for stochastic non-autonomous nonclassical diffusion equation on the bounded domain.We show the uniform estimate of solution under the appropriate assumptions for two the nonlinear terms of the equation.The method of orthogonal spectral decomposition is used to prove the asymptotic compactness of the solution of the equation in the H_(0)^(1)(O),and it is concluded that the non-autonomous stochastic dynamic system generated by this equation has a unique pullback random attractor under the Wong-Zakai approximations.

关 键 词：非经典扩散方程 拉回随机吸引子 Wong-Zakai逼近 

分 类 号：O175[理学—数学]