A Stochastic Conservation Law with Nonhomogeneous Dirichlet Boundary Conditions

Kazuo Kobayasi; Dai Noboriguchi

doi:10.1007/s40306-015-0157-5

A Stochastic Conservation Law with Nonhomogeneous Dirichlet Boundary Conditions

Kazuo Kobayasi, Dai Noboriguchi^*

^*Corresponding author for this work

Waseda University Senior High School

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

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.

Original language	English
Pages (from-to)	607-632
Number of pages	26
Journal	Acta Mathematica Vietnamica
Volume	41
Issue number	4
DOIs	https://doi.org/10.1007/s40306-015-0157-5
Publication status	Published - 2016 Dec 1

Keywords

Conservation laws
Initial-boundary value problem
Kinetic formulation
Stochastic partial differential equations

ASJC Scopus subject areas

Mathematics(all)

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10.1007/s40306-015-0157-5

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N2 - 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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KW - Kinetic formulation

KW - Stochastic partial differential equations

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A Stochastic Conservation Law with Nonhomogeneous Dirichlet Boundary Conditions

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Keywords

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