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Article

Kettani, Perla El ; Hilhorst, Danielle ; Lee, Kai
A well-posedness result for a mass conserved Allen-Cahn equation with nonlinear diffusion. (English). In: Mikula, Karol (ed.): Proceedings of Equadiff 14. Conference on Differential Equations and Their Applications, Bratislava, July 24-28, 2017. Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing, Bratislava, 2017. pp. 201-210
MSC: 35K55, 35K57, 60H15, 60H30
Keywords:
Stochastic nonlocal reaction-diffusion equation, monotonicity method, conservation of mass
Summary:
In this paper, we prove the existence and uniqueness of the solution of the initial boundary value problem for a stochastic mass conserved Allen-Cahn equation with nonlinear diffusion together with a homogeneous Neumann 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.
References:
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