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Article Dans Une Revue Stochastic Analysis and Applications Année : 2020

Well-posedness result for a system of random heat equation coupled with a multiplicative stochastic Barenblatt equation

Résumé

In this paper, a stochastic nonlinear evolution system under Neumann boundary conditions is investigated. Precisely, we are interested in finding an existence and uniqueness result for a system of random heat equation coupled with a Barenblatt's type equation with a multiplicative stochastic force in the sense of Itô. To do so, we investigate in a first step the case of an additive noise through a semi-implicit in time discretization of the system. This allows us to show the well-posedness of the system in the additive case. In a second step, the derivation of continuous dependence estimates of the solution with respect to the data allows us to show the desired existence and uniqueness result for the multiplicative case.
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Dates et versions

hal-02361179 , version 1 (13-11-2019)

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  • HAL Id : hal-02361179 , version 1

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Caroline Bauzet, Frédéric Lebon, Ali Maitlo, Aleksandra Zimmermann. Well-posedness result for a system of random heat equation coupled with a multiplicative stochastic Barenblatt equation. Stochastic Analysis and Applications, inPress. ⟨hal-02361179⟩
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