Coupled Stochastic Allen-Cahn equations: Existence and Uniqueness

2022/03/08 by Phu, Tran Hoa
#Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2203.04280

Abstract

In this paper, we concern a system of stochastic PDE's. Our system consists of two components. Each component evolves according to the sotchastic Allen-Cahn equation with a symmetric double well potential and with addtional small space-time white noise. The two components interact with each other by an attractive linear force. We aim to give a global existence and uniqueness result in a space of continuous functions on ℝ × ℝ⁺. We apply methods proposed by Doering \citeDoering1987.

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