论文标题
耦合随机allen-cahn方程：存在与独特性
Coupled Stochastic Allen-Cahn equations: Existence and Uniqueness
论文作者
论文摘要
在本文中，我们涉及一个随机PDE的系统。我们的系统由两个组件组成。每个组件根据具有对称的双井潜力和额外的小时时间白噪声的sotchastic allen-cahn方程而演变。这两个组件通过有吸引力的线性力相互相互作用。我们的目的是给出全局的存在和独特性，从而在$ \ mathbb {r} \ times \ times \ mathbb {r}^+$上获得连续功能的空间。我们应用Doering \ Cite {Doering1987}提出的方法。
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}.
