Systems of reflected quasilinear stochastic PDEs in a convex domain

Wissal Sabbagh; Tusheng Zhang

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arXiv · 1603.08610

Systems of reflected quasilinear stochastic PDEs in a convex domain

Wissal Sabbagh·Tusheng Zhang

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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.

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Wissal Sabbagh, Tusheng Zhang. 2016-03-29. Systems of reflected quasilinear stochastic PDEs in a convex domain. https://arxiv.org/abs/1603.08610

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