Weak convergence of attractors of reaction-diffusion systems with randomly oscillating coefficients

We consider reaction-diffusion systems with random rapidly oscillating coefficient. We do not assume any Lipschitz condition for the nonlinear function in the system, so, the uniqueness theorem for the corresponding initial-value problem may not hold for the considered reaction-diffusion system. Under the assumption that the random function is ergodic and statistically homogeneous in space variables we prove that the trajectory attractors of these systems tend in a weak sense to the trajectory attractors of the homogenized reaction-diffusion systems whose coefficient is the average of the corresponding term of the original systems.