Abstract The main concern of this paper is the study of degenerate sweeping process involving uniform prox-regular sets via an unconstrained differential inclusion by showing that the sets of solutions of the two problems coincide. This principle of reduction to unconstrained evolution problem can be seen as a penalization of the subdifferential of the distance function. Using this reduction technique, an existence and uniqueness result of a Lipschitz perturbed version of the degenerate sweeping process is proved in the finite dimensional setting. An application is given to quasistatic unilateral dynamics in nonsmooth mechanics where the moving set is described by a finite number of inequalities. We provide sufficient verifiable conditions ensuring both the prox-regularity and the Lipschitz continuity with respect to the Hausdorff distance of the moving set.

中文翻译：

---

通过无约束演化问题的非凸退化扫掠过程的适定性

摘要 本文的主要关注点是通过无约束微分包含研究涉及一致近正则集的退化扫描过程，通过证明两个问题的解集重合。这种归约到无约束进化问题的原理可以看作是对距离函数的次微分的惩罚。使用这种减少技术，在有限维设置中证明了退化扫描过程的 Lipschitz 扰动版本的存在性和唯一性结果。给出了非光滑力学中准静态单边动力学的应用，其中运动集由有限数量的不等式描述。