On a stochastic first order hyperbolic equation in a bounded domain
Guy Vallet and Petra Wittbold
Abstract: In this paper, we are interested in the stochastic perturbation of a first order hyperbolic equation of nonlinear type. In order to illustrate our purposes, we have chosen a scalar conservation law in a bounded domain with homogeneous Dirichlet condition on the boundary. Using the concept of measure-valued solutions and Kruzhkov's entropy formulation, a result of existence and uniqueness of the entropy solution is given.