关于网络上带乘性噪声的随机Allen-Cahn方程
偏微分方程分析
2021-04-28 v2 概率论
摘要
我们考虑定义在由有限图表示的有限网络上的随机 Allen-Cahn 方程组。在图的每条边上给定一个由乘性高斯噪声驱动的随机 Allen-Cahn 方程，其势垒高度可能不同，并在顶点处补充连续性条件和 Kirchhoff 型定律。利用 Banach 空间中随机演化方程的半群方法，我们得到了在图上连续函数空间中具有样本路径的解的存在唯一性。我们还证明了解更精确的时空正则性。
引用
@article{arxiv.2011.11359,
title = {On the stochastic Allen-Cahn equation on networks with multiplicative noise},
author = {Mihály Kovács and Eszter Sikolya},
journal= {arXiv preprint arXiv:2011.11359},
year = {2021}
}
备注
The proof of Corollary 3.7 in the original submission was incomplete as only the continuity of the embeddings are verified in the proof but the denseness of the embeddings are not. In the present version we provide a new poof of Proposition 3.8 that is independent of Corollary 3.7. This way, we may use Proposition 3.8 to fill in the gap in the proof of Corollary 3.7