In this paper, a moving boundary technique is developed to investigate wave runup and rundown with depth-integratedequations. Highly nonlinear and weakly dispersive equations are solved using a high-order finite difference scheme. An eddyviscosity model is adopted for wave breaking so as to investigate breaking wave runup. The moving boundary technique utilizeslinear extrapolation t...

We consider a stochastic perturbation of a moving boundary problem proposed by Ludford and Stewart and studied by Caffarelli and Vazquez. We prove existence and uniqueness.