The equivalence theorem of kinetic solutions and entropy solutions for stochastic scalar conservation laws

Dai Noboriguchi

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Abstract

In this paper, we prove the equivalence of kinetic solutions and entropy solutions for the initialboundary value problem with a non-homogeneous boundary condition for a multi-dimensional scalar first-order conservation law with a multiplicative noise. We somewhat generalized the definitions of kinetic solutions and of entropy solutions given in Kobayasi and Noboriguchi [8] and Bauzet, Vallet and Wittobolt [1], respectively.

Original languageEnglish
Pages (from-to)575-587
Number of pages13
JournalTokyo Journal of Mathematics
Volume38
Issue number2
DOIs
Publication statusPublished - 2015 Dec 1

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Keywords

  • Conservation laws
  • Entropy solution
  • Kinetic solution

ASJC Scopus subject areas

  • Mathematics(all)

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