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A Stochastic Conservation Law with Nonhomogeneous Dirichlet Boundary Conditions
Kazuo Kobayasi, Dai Noboriguchi

 

Abstract

This paper discusses the initial-boundary value problem (with a nonhomogeneous boundary condition) for a multi-dimensional scalar first-order conservation law with a multiplicative noise. One introduces a notion of kinetic formulations in which the kinetic defect measures on the boundary of a domain are truncated. In such a kinetic formulation, one obtains a result of uniqueness and existence. The unique solution is the limit of the solution of the stochastic parabolic approximation. 

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