Systems of semilinear parabolic variational inequalities with   time-dependent convex obstacles
  We consider a system of seminlinear parabolic variational inequalities with time-dependent convex obstacles. We prove the existence and uniqueness of its solution. We also provide a stochastic representation of the solution and show that it can be approximated by the penalization method. Our proofs are based upon probabilistic methods from the theory of Markov processes and the theory of backward stochastic differential equations. 
Tomasz Klimsiak, Andrzej Rozkosz, Leszek Slominski
math.AP