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arXiv · 1506.05758

A stochastic conservation law with nonhomogeneous Dirichlet boundary conditions

Kazuo Kobayasi·Dai Noboriguchi
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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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Kazuo Kobayasi, Dai Noboriguchi. 2015-06-18. A stochastic conservation law with nonhomogeneous Dirichlet boundary conditions. https://arxiv.org/abs/1506.05758

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