Discrete reaction-diffusion system with stochastic dynamical boundary conditions: convergence results
Abstract
A space discrete approximation to a highly nonlinear reaction-diffusion system endowed with a stochastic dynamical boundary condition is analyzed and the convergence of the discrete scheme to the solution to the corresponding continuum random system is established. A splitting strategy allows us to decompose the random system into a space-discrete heat equation with a stochastic boundary condition, and a nonlinear and nonlocal space-discrete differential system coupled with the first one and with deterministic initial and boundary conditions. The convergence result is obtained by first establishing some a priori estimates for both space-discrete splitted variables and then exploiting compact embedding theorems for time-space Besov spaces on the positive lattice. The convergence of a fully discrete approximation of the random system is also discussed.
Cite
@article{arxiv.2507.09278,
title = {Discrete reaction-diffusion system with stochastic dynamical boundary conditions: convergence results},
author = {Francesca Arceci and Francesco Carlo De Vecchi and Daniela Morale and Stefania Ugolini},
journal= {arXiv preprint arXiv:2507.09278},
year = {2025}
}