On a Stochastic First Order Hyperbolic Equation in a Bounded Domain

  title={On a Stochastic First Order Hyperbolic Equation in a Bounded Domain},
  author={Guy Vallet and Petra Wittbold},
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. keywords : Stochastic PDE, first-order hyperbolic problems, bounded domain… CONTINUE READING
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