Variational convergence of nonlocal integrodifferential diffusion problems of gradient flow type

Omar Anza Hafsa (1) , Jean-Philippe Mandallena (1) , Gérard Michaille (1)

1 MIPA - Mathématiques, Informatique, Physique, et Applications / Université de Nîmes

In this paper we continue our study of nonlocal problems of gradient flow type that we developed in our previous papers [AHMM23, AHMM24]. We consider here nonlocal integrodifferential diffusion problems. We present existence, uniqueness and compactness results and investigate stochastic homogenization.

Keywords: Integrodifferential nonlocal diffusion equations; Mosco-convergence; Γ-convergence; Convergence of integrodifferential nonlocal diffusion equations; stochastic homogenization

Domains: Mathematics [math]; Analysis of PDEs [math.AP]

Omar Anza Hafsa, Jean-Philippe Mandallena, Gérard Michaille. Variational convergence of nonlocal integrodifferential diffusion problems of gradient flow type. 2024. ⟨hal-04553370⟩