White noise driven SPDEs with oblique reflection: Existence and uniqueness

摘要

In this paper, we study existence and uniqueness to multidimensional reflected stochastic partial differential equations in a convex domain, allowing for oblique direction of reflection. The method is to use approximations of penalized systems of SPDEs. Using a priori estimates for the solutions of the penalized systems of SPDEs, we establish the existence of solutions of white noise driven SPDEs with oblique reflection. The uniqueness is proved by using the geometric property of oblique reflection. (C) 2019 Elsevier Inc. All rights reserved.