# American Institute of Mathematical Sciences

November  2018, 38(11): 5615-5648. doi: 10.3934/dcds.2018246

## 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

Received  December 2017 Revised  June 2018 Published  August 2018

Fund Project: 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

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.

Citation: Perla El Kettani, Danielle Hilhorst, Kai Lee. A stochastic mass conserved reaction-diffusion equation with nonlinear diffusion. Discrete & Continuous Dynamical Systems - A, 2018, 38 (11) : 5615-5648. doi: 10.3934/dcds.2018246
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