Well-posedness result for a system of random heat equation coupled with a multiplicative stochastic Barenblatt equation - Archive ouverte HAL Access content directly
Journal Articles Stochastic Analysis and Applications Year : 2020

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

Abstract

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.
Fichier principal
Vignette du fichier
BLMZ_10:11:19.pdf (454.97 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

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

Identifiers

  • HAL Id : hal-02361179 , version 1

Cite

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⟩
166 View
83 Download

Share

Gmail Facebook X LinkedIn More