Applied Mathematics and Optimization, Vol.58, No.1, 29-67, 2008
On the stochastic wave equation with nonlinear damping
We discuss an initial boundary value problem for the stochastic wave equation with nonlinear damping. We establish the existence and uniqueness of a solution. Our method for the existence of pathwise solutions consists of regularization of the equation and data, the Galerkin approximation and an elementary measure-theoretic argument. We also prove the existence of an invariant measure when the equation has pure nonlinear damping.
Keywords:wave equation;nonlinear damping;initial boundary value problem;Brownian motion;invariant measure