Original version
Networks and Heterogeneous Media. 2022, 17 (5):719, DOI: https://doi.org/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.