This paper is devoted to the study of a new class of implicit state-dependent sweeping processes with history-dependent operators. Based on the methods of convex analysis, we prove the equivalence of the history/state dependent implicit sweeping process and a nonlinear differential equation, which, through a fixed point argument for history-dependent operators, enables us to prove the existence, uniqueness, and continuous dependence of the solution in a very general framework. Moreover, we present some new convergence results with respect to perturbations in the data, including perturbations of the associated moving sets. Finally, the theoretical results are applied to prove the well-posedness of a history-dependent quasi-static contact problem.

中文翻译：

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历史/状态相关的隐式清除过程的良好状态

本文致力于研究一类具有历史相关算子的隐式状态相关扫描过程。基于凸分析的方法，我们证明了历史/状态相关的隐式扫描过程与非线性微分方程的等价性，该方程通过对历史相关算子的不动点论证，使我们能够证明存在性、唯一性和解决方案在非常通用的框架中的连续依赖性。此外，我们提出了一些关于数据扰动的新收敛结果，包括相关移动集的扰动。最后，将理论结果应用于证明历史相关准静态接触问题的适定性。