Well-posedness for the coupling of a random heat equation with a multiplicative stochastic Barenblatt equation
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 Itô. 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.
- Publication:
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arXiv e-prints
- Pub Date:
- December 2019
- DOI:
- 10.48550/arXiv.1912.09728
- arXiv:
- arXiv:1912.09728
- Bibcode:
- 2019arXiv191209728B
- Keywords:
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- Mathematics - Analysis of PDEs