Variational convergence of nonlocal integrodifferential diffusion problems of gradient flow type

In this paper, we continue our study of nonlocal problems of gradient flow type that we developed in our previous papers [O.Anza Hafsa, J.-P.Mandallena, G. Michaille, Nonlocal time delays reaction-diffusion problems of gradient flow type: Existence, stochastic homogenization, Evol.Equ.Control Theory 17 (2026) 23-61] and [O.Anza Hafsa, J.-P.Mandallena, G. Michaille, Stochastic homogenization of nonlocal reaction-diffusion problems of gradient flow type, J. Elliptic Parabol.Equ. 10 (2024) 415-474].We consider here nonlocal integrodifferential diffusion problems.We present existence, uniqueness and compactness results and investigate stochastic homogenization.