随机反应扩散方程的随机吸引子的高阶稳定性

Higher-order Stability of Attractors for Stochastic Reaction-Diffusion Equation

本文研究带加性白噪声的随机反应扩散方程的随机吸引子关于噪声强度的稳定性。首先,在非线性函数满足更一般条件下,在初始空间L^(2)(R^(N))中获得随机微分方程的解收敛到确定方程的解,从而得到随机吸引子的上半连续性;然后,利用非线性分解和差分估计,证明L^(p)(R^(N))(p>2)空间中解的收敛性和随机吸引子的上半连续性,其中p是非线性函数的增长指数。

The stability of random attractors of the stochastic reaction-diffusion equation with additive white noise is studied.First,with a general assumption on the nonlinear term,the solutions of the stochastic differential equation converge to the solutions of the deterministic equation in the initial space L^(2)(R^(N)),and the upper semi-continuity of the random attractors is obtained.In particular,by using the nonlinear decomposition and the difference estimation,we technically obtain the convergence of solutions and the upper semi-continuity of random attractors in L^(p)(R^(N))(p>2),where p is the growth index of the nonlinear function.