Large deviations for fast transport stochastic RDEs with applications to the exit problem

TL;DR

This paper investigates large deviation principles for stochastic reaction-diffusion equations with multiple reaction terms under different scaling regimes, focusing on the exit problem in the context of fast transport.

Contribution

It introduces a novel analysis of large deviations for reaction-diffusion equations with mixed deterministic and random reaction terms under specific scaling regimes.

Findings

Derived large deviation estimates for the exit time and location.

Characterized the asymptotic behavior of solutions in the fast diffusion regime.

Provided applications to boundary exit problems in stochastic PDEs.

Abstract

We study reaction diffusion equations with a deterministic reaction term as well as two random reaction terms, one that acts on the interior of the domain, and another that acts only on the boundary of the domain. We are interested in the regime where the relative sizes of the diffusion and reaction terms are different. Specifically, we consider the case where the diffusion rate is much larger than the rate of reaction, and the deterministic rate of reaction is much larger than either of the random rate of reactions.