Systems of reflected quasilinear stochastic PDEs in a convex domain

TL;DR

This paper establishes existence and uniqueness for systems of reflected quasilinear stochastic PDEs in convex domains, using probabilistic methods involving backward doubly stochastic differential equations.

Contribution

It introduces a novel probabilistic approach to solve reflected quasilinear stochastic PDE systems in convex domains, extending previous methods.

Findings

Proves existence and uniqueness of solutions

Expresses solutions via backward doubly stochastic differential equations

Characterizes solutions with a pair (u,{ u}) satisfying specific conditions

Abstract

This paper presents existence and uniqueness results for reflected system of quasilinear stochastic partial differential equations in a convex domain D from Rk. The method is based on the probabilistic interpretation of the solution by using the backward doubly stochastic differential equation. The solution is expressed as a pair (u,{\nu}) where u is a predictable continuous process which takes values in a proper Sobolev space and {\nu} is a random signed regular measure satisfying the minimal Skohorod condition.