Global solutions to the stochastic heat equation with superlinear accretive reaction term and superlinear multiplicative noise term on a bounded spatial domain

TL;DR

This paper establishes conditions under which solutions to a stochastic reaction-diffusion equation with superlinear growth in reaction and noise terms remain globally bounded, preventing explosion on bounded domains.

Contribution

It provides new sufficient conditions ensuring global existence of solutions for stochastic heat equations with superlinear reaction and noise terms.

Findings

Solutions remain bounded under specified conditions

Superlinear growth in reaction and noise terms is permissible

Conditions prevent solution explosion on bounded domains

Abstract

We describe sufficient conditions on the reaction terms and multiplicative noise terms of a stochastic reaction-diffusion equation that guarantee that the solutions never explode. Both the reaction term and multiplicative noise terms are allowed to grow superlinearly.