耦合随机Allen-Cahn方程的存在性与唯一性
Coupled Stochastic Allen-Cahn equations: Existence and Uniqueness
摘要：
本文研究一类随机偏微分方程组。我们的系统由两个部分组成。每个分量的演化遵循具有对称双势阱和附加小时空白噪声的随机Allen-Cahn方程。这两个部件通过吸引力相互作用。我们的目标是给出$\mathbb{R} \times \mathbb{R}^+$上连续函数空间的整体存在唯一性结果。我们采用Doering \cite{Doering1987}提出的方法。
英文摘要：
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}.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
