A Stochastic Conservation Law with Nonhomogeneous Dirichlet Boundary Conditions

Kazuo Kobayasi, Dai Noboriguchi

Research output: Contribution to journalArticle

3 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 607-632 26 Acta Mathematica Vietnamica 41 4 https://doi.org/10.1007/s40306-015-0157-5 Published - 2016 Dec 1

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Kinetic Formulation
Nonhomogeneous Boundary Conditions
Conservation Laws
Dirichlet Boundary Conditions
Multiplicative Noise
Unique Solution
Initial-boundary-value Problem
Existence and Uniqueness
Defects
Kinetics
Scalar
First-order
Approximation

Keywords

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

ASJC Scopus subject areas

• Mathematics(all)

Cite this

In: Acta Mathematica Vietnamica, Vol. 41, No. 4, 01.12.2016, p. 607-632.

Research output: Contribution to journalArticle

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