具有有限回撤的准连续型扫荡过程
动力系统
2024-10-25 v3
摘要
本文旨在双重目标。一方面，我们证明了由均匀准连续型移动集（具有局部有限回撤）驱动的 Moreau 扫荡过程具有唯一解，前提是准连续性系数大于驱动集任何跳跃的大小。另一方面，我们展示了局部有限回撤情况可以容易地简化为 1-Lipschitz 连续情况：我们首先通过所谓“catching-up 算法”求解 Lipschitz 连续情况，然后通过一种用于处理准连续集族函数的重参数化技术，将局部有限回撤情况归约为 Lipschitz 情形。
关键词
引用
@article{arxiv.2407.09354,
title = {Prox-regular sweeping processes with bounded retraction},
author = {Vincenzo Recupero},
journal= {arXiv preprint arXiv:2407.09354},
year = {2024}
}
备注
Other misprints have been corrected. arXiv admin note: text overlap with arXiv:2008.13623. Author's comment: the present paper is very different from arXiv:2008.13623: it deals with sweeping processes in a prox-regular setting, while arXiv:2008.13623 deals with the easier convex setting