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<p>In this paper, we study the well-posedness of state-dependent and state-independent sweeping processes driven by prox-regular sets and perturbed by a history-dependent operator. Our approach, based on an enhanced version of Gronwall’s lemma and fixed-point arguments, provides an efficient framework for analyzing sweeping processes. In particular, our findings recover all existing results for the class of Volterra sweeping processes and provide new insights into history-dependent sweeping processes. Finally, we apply our theoretical results to establish the well-posedness of a viscoelastic model with long memory.</p>

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A Fixed-Point Approach to History-Dependent Sweeping Processes

  • 期刊论文

  • 发表日期：

    2025年5月27日

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  • Matías Godoy,
  • Manuel Torres-Valdebenito,
  • Emilio Vilches

摘要

In this paper, we study the well-posedness of state-dependent and state-independent sweeping processes driven by prox-regular sets and perturbed by a history-dependent operator. Our approach, based on an enhanced version of Gronwall’s lemma and fixed-point arguments, provides an efficient framework for analyzing sweeping processes. In particular, our findings recover all existing results for the class of Volterra sweeping processes and provide new insights into history-dependent sweeping processes. Finally, we apply our theoretical results to establish the well-posedness of a viscoelastic model with long memory.