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arXiv · 1912.09728

Well-posedness for the coupling of a random heat equation with a multiplicative stochastic Barenblatt equation

Caroline Bauzet·Frédéric Lebon·Asghar Ali Maitlo·Aleksandra Zimmermann
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Abstract

In this contribution, a stochastic nonlinear evolution system under Neumann boundary conditions is investigated. Precisely, we are interested in finding an existence and uniqueness result for a random heat equation coupled with a Barenblatt's type equation with a multiplicative stochastic force in the sense of It\^o. In a first step we establish well-posedness in the case of an additive noise through a semi-implicit time discretization of the system. 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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Caroline Bauzet, Frédéric Lebon, Asghar Ali Maitlo, Aleksandra Zimmermann. 2019-12-20. Well-posedness for the coupling of a random heat equation with a multiplicative stochastic Barenblatt equation. https://arxiv.org/abs/1912.09728

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