Stochastic variational inequalities for a wave equation

Abstract

We discuss evolution variational inequalities for a wave equation with unilateral constraint on the velocity. Both deterministic and stochastic obstacle problems will be considered. For deterministic obstacles, we will focus on the case which is directly related to stochastic equations. This makes it necessary to formulate a new definition of a solution. Based on this definition, we will establish existence and uniqueness of a solution to both deterministic and stochastic problems.