A stochastic conservation law with nonhomogeneous Dirichlet boundary conditions
Mathematical Physics
2015-06-19 v1 math.MP
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.
Keywords
Cite
@article{arxiv.1506.05758,
title = {A stochastic conservation law with nonhomogeneous Dirichlet boundary conditions},
author = {Kazuo Kobayasi and Dai Noboriguchi},
journal= {arXiv preprint arXiv:1506.05758},
year = {2015}
}