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

Kazuo Kobayasi, Dai Noboriguchi

研究成果: Article査読

抄録

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].

本文言語English
ページ(範囲)1416-1458
ページ数43
ジャーナルJournal of Mathematical Analysis and Applications
461
2
DOI
出版ステータスPublished - 2018 5 15

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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