@article{a487dab713384c41a6cac10619361a5f,
title = "A Stochastic Conservation Law with Nonhomogeneous Dirichlet Boundary Conditions",
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 = "Conservation laws, Initial-boundary value problem, Kinetic formulation, Stochastic partial differential equations",
author = "Kazuo Kobayasi and Dai Noboriguchi",
note = "Publisher Copyright: {\textcopyright} 2015, Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore. Copyright: Copyright 2016 Elsevier B.V., All rights reserved.",
year = "2016",
month = dec,
day = "1",
doi = "10.1007/s40306-015-0157-5",
language = "English",
volume = "41",
pages = "607--632",
journal = "Acta Mathematica Vietnamica",
issn = "0251-4184",
publisher = "Springer Verlag",
number = "4",
}