A Fixed-Point Approach to History-Dependent Sweeping Processes

Matías Godoy (), Manuel Torres-Valdebenito () and Emilio Vilches ()
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Matías Godoy: Universidad San Sebastián
Manuel Torres-Valdebenito: Universidad de Chile
Emilio Vilches: Universidad de O’Higgins

Journal of Optimization Theory and Applications, 2025, vol. 206, issue 2, No 16, 22 pages

Abstract: Abstract 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.

Keywords: Sweeping process; Fixed point theory; History-dependent operator; prox-regular set; 34A60; 49J52; 49J53 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02714-4

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