Well-posedness for stochastic scalar conservation laws with the initial-boundary condition

Kazuo Kobayasi, Dai Noboriguchi

Research output: Contribution to journalArticle

Abstract

In this paper, we are interested in the initial-(non-homogeneous) Dirichlet boundary value problem for a multi-dimensional scalar non-linear conservation law with a multiplicative stochastic forcing. We introduce a notion of “renormalized” kinetic formulations in which the kinetic defect measures on the boundary of a domain are truncated. In such a kinetic formulation we establish a result of well-posedness of the initial-boundary value problem under only the assumptions (H1), (H2) and (H3) stated below, which are very similar ones in [6].

Original languageEnglish
Pages (from-to)1416-1458
Number of pages43
JournalJournal of Mathematical Analysis and Applications
Volume461
Issue number2
DOIs
Publication statusPublished - 2018 May 15
Externally publishedYes

Keywords

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

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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