@article{Bendahmane2022, 
author = {Mostafa Bendahmane and Kenneth H. Karlsen},
title = {Martingale solutions of stochastic nonlocal cross-diffusion systems},
year = {2022},
journal = {Networks and Heterogeneous Media},
volume = {17},
number = {5},
pages = {719-752},
keywords = {Stochastic partial differential equation, cross-diffusion system, existence, martingale solution, population dynamics},
url = {https://www.sciopen.com/article/10.3934/nhm.2022024},
doi = {10.3934/nhm.2022024},
abstract = {We establish the existence of solutions for a class of stochastic reaction-diffusion systems with cross-diffusion terms modeling interspecific competition between two populations. More precisely, we prove the existence of weak martingale solutions employing appropriate Faedo-Galerkin approximations and the stochastic compactness method. The nonnegativity of solutions is proved by a stochastic adaptation of the well-known Stampacchia approach.}
}