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Preprints, Working Papers, ... Year : 2020

Uniqueness of the entropy solution of a stochastic conservation law with a Q-Brownian motion

Yueyuan Gao
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  • PersonId : 954152
Danielle Hilhorst
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  • PersonId : 834048

Abstract

In this paper, we prove the uniqueness of the entropy solution for a first order stochastic conservation law with a multiplicative source term involving a Q-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 in turn coincides with its unique entropy solution.
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Dates and versions

hal-02159743 , version 1 (19-06-2019)
hal-02159743 , version 2 (19-02-2020)

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  • HAL Id : hal-02159743 , version 2

Cite

Tadahisa Funaki, Yueyuan Gao, Danielle Hilhorst. Uniqueness of the entropy solution of a stochastic conservation law with a Q-Brownian motion. 2020. ⟨hal-02159743v2⟩
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