Global in time solutions to stochastic reaction-diffusion systems with superlinear reactions satisfying a triangular control of mass

TL;DR

This paper proves that stochastic reaction-diffusion systems with superlinear reactions and a triangular mass-control structure have global solutions when perturbed by multiplicative noise, extending deterministic results to stochastic models.

Contribution

It demonstrates that multiplicative noise ensures global existence of solutions for reaction-diffusion systems with mass-control, which was previously unresolved in stochastic settings.

Findings

Solutions exist globally under stochastic perturbations with mass-control.

The approach applies to models in chemistry and biology.

Stochastic noise stabilizes systems that may blow up in deterministic cases.

Abstract

We study systems of reaction-diffusion equations perturbed by multiplicative noise, where the reaction terms satisfy quasipositivity, a triangular mass-control structure, and polynomial growth. Our results apply to a broad class of reaction-diffusion systems arising, most notably, in chemistry and biology. In the deterministic setting these assumptions are known to guarantee the global existence of solutions. In the stochastic setting, however, reaction-diffusion systems have typically been analyzed under different assumptions on the reactions that preclude many natural models, such as chemical reaction systems, and the question of global existence and uniqueness under a mass-control structure has remained open. In this work, we show that stochastically perturbing reaction-diffusion systems with triangular mass control by suitable multiplicative noise leads to solutions that exist for all time.