A stochastic mass conserved reaction-diffusion equation with nonlinear diffusion

Perla El Kettani; Danielle Hilhorst; Kai Lee

doi:10.3934/dcds.2018246

Article Contents

2018, Volume 38, Issue 11: 5615-5648. Doi: 10.3934/dcds.2018246

This issue Previous Article Hopf-Tsuji-Sullivan dichotomy for quotients of Hadamard spaces with a rank one isometry Next Article Averaging principle for stochastic Kuramoto-Sivashinsky equation with a fast oscillation

A stochastic mass conserved reaction-diffusion equation with nonlinear diffusion

1.
Laboratoire de Mathématique, Analyse Numérique et EDP, University of Paris-Sud, F-91405 Orsay Cedex, France
2.
CNRS and Laboratoire de Mathématique, Analyse Numérique et EDP, University of Paris-Sud, F-91405 Orsay Cedex, France
3.
Graduate School of Mathematical Sciences, University of Tokyo, Komaba, Tokyo 153-8914, Japan

* Corresponding author: Danielle Hilhorst
* Corresponding author: Danielle Hilhorst

Received: December 2017

Revised: June 2018

Published: August 2018

The first author is supported by a public grant as part of the Investissement d'avenir project, reference ANR-11-LABX-0056-LMH, LabEx LMH

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Abstract

In this paper, we prove a well posedness result for an initial boundary value problem for a stochastic nonlocal reaction-diffusion equation with nonlinear diffusion together with a nul-flux boundary condition in an open bounded domain of $\mathbb{R}^n$ with a smooth boundary. We suppose that the additive noise is induced by a Q-Brownian motion.

Keywords:

Stochastic nonlocal reaction-diffusion equation,
monotonicity method,
conservation of mass.

Mathematics Subject Classification: Primary: 60H15, 60H30, 35K55, 35K57.

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