Systems of reflected quasilinear stochastic PDEs in a convex domain

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.