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arXiv · 2203.04280

Coupled Stochastic Allen-Cahn equations: Existence and Uniqueness

Tran Hoa Phu
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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 $\mathbb{R} \times \mathbb{R}^+$. We apply methods proposed by Doering \cite{Doering1987}.

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Tran Hoa Phu. 2022-03-08. Coupled Stochastic Allen-Cahn equations: Existence and Uniqueness. https://arxiv.org/abs/2203.04280

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