In this paper we consider the homogenization problem of nonlinear evolution equations with space-time nonlocality, the problems are given by Beltritti and Rossi J. Math. Anal. Appl. 455, 1470–1504 (2017). When the integral kernel J(x, t; y, s) is re-scaled in a suitable way and the oscillation coefficient ν(x, t; y, s) possesses periodic and stationary structure, we show that the solutions uɛ(x, t) to the perturbed equations converge to u0(x, t), the solution of corresponding local nonlinear parabolic equation as scale parameter ɛ → 0+. Then for the nonlocal linear index p = 2 we give the optimal convergence rate such that ‖uε−u0‖L2(Rd×(0,T))≤Cε. Furthermore, we obtain that the normalized difference 1εuε(x,t)−u0(x,t)−χ(xε,tε2)∇xu0(x,t) converges to a solution of an SPDE with additive noise and constant coefficients. Finally, we give some numerical formats for solving nonlocal space-time homogenization.
Chen et al. (Fri,) studied this question.