Existence and uniqueness of the entropy solution of a stochastic conservation law with a Q-Brownian motion

Tadahisa Funaki, Yueyuan Gao*, Danielle Hilhorst

*この研究の対応する著者

研究成果: Article査読

抄録

In this paper, we prove the existence and uniqueness of the entropy solution for a first-order stochastic conservation law with a multiplicative source term involving a (Formula presented.) -Brownian motion. After having defined a measure-valued weak entropy solution of the stochastic conservation law, we present the Kato inequality, and as a corollary, we deduce the uniqueness of the measure-valued weak entropy solution, which coincides with the unique weak entropy solution of the problem. The Kato inequality is proved by a doubling of variables method; to that purpose, we prove the existence and the uniqueness of the strong solution of an associated stochastic nonlinear parabolic problem by means of an implicit time discretization scheme; we also prove its convergence to a measure-valued entropy solution of the stochastic conservation law, which proves the existence of the measure-valued entropy solution.

本文言語English
ページ(範囲)5860-5886
ページ数27
ジャーナルMathematical Methods in the Applied Sciences
43
9
DOI
出版ステータスPublished - 2020 6 1

ASJC Scopus subject areas

  • 数学 (全般)
  • 工学(全般)

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