A Stochastic Conservation Law with Nonhomogeneous Dirichlet Boundary Conditions

Kazuo Kobayasi, Dai Noboriguchi*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


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 languageEnglish
Pages (from-to)607-632
Number of pages26
JournalActa Mathematica Vietnamica
Issue number4
Publication statusPublished - 2016 Dec 1


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

ASJC Scopus subject areas

  • Mathematics(all)


Dive into the research topics of 'A Stochastic Conservation Law with Nonhomogeneous Dirichlet Boundary Conditions'. Together they form a unique fingerprint.

Cite this