Homogenization of nonlocal equations in randomly evolving media. Diffusion approximation

The paper deals with homogenization and higher order approximations of solutions to nonlocal evolution equations of convolution type whose coefficients are periodic in the spatial variables and random stationary in time. We assume that the convolution kernel has finite moments up to order three. Under proper mixing assumptions, we study the limit behavior of the normalized difference between solutions of the original and the homogenized problems and show that this difference converges to the solution of a linear stochastic partial differential equation.

💡 Research Summary

The paper investigates the homogenization and diffusion‑approximation of a class of non‑local evolution equations of convolution type whose coefficients are periodic in the spatial variables and stationary random in time. The main equation under study is

\