Stochastic reaction-diffusion systems with Hölder continuous multiplicative noise

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 Hölder continuous multiplicative noise. Under additional assumptions on the coefficients, we also prove positivity of the solutions.

21 pages

References in corpus (3)

• Nonuniqueness for a parabolic SPDE with $\frac{3}{4}-\epsilon$-Hölder diffusion coefficients
• On a Class of Martingale Problems on Banach Spaces
• Pathwise uniqueness for stochastic heat equations with Hölder continuous coefficients: the white noise case

Cited by in corpus (1)

• On a Class of Martingale Problems on Banach Spaces