Stochastic reaction-diffusion systems with H\"older continuous multiplicative noise

TL;DR

This paper establishes the existence, uniqueness, and positivity of solutions for stochastic reaction-diffusion systems influenced by H"older continuous multiplicative noise, advancing understanding of such complex stochastic PDEs.

Contribution

It proves pathwise uniqueness, strong existence, and positivity of solutions for reaction-diffusion systems with H"older continuous noise, extending previous results to more general noise conditions.

Findings

Proved pathwise uniqueness of solutions.

Established strong existence of solutions.

Demonstrated positivity under certain conditions.

Abstract

We prove pathwise uniqueness and strong existence of solutions for stochastic reaction-diffusion systems with locally Lipschitz continuous reaction term of polynomial growth and H\"older continuous multiplicative noise. Under additional assumptions on the coefficients, we also prove positivity of the solutions.