A fixed-point approach to history-dependent sweeping processes
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910764700270592 |
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| author | Godoy, Matías Torres-Valdebenito, Manuel Vilches, Emilio |
| author_facet | Godoy, Matías Torres-Valdebenito, Manuel Vilches, Emilio |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_19210 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A fixed-point approach to history-dependent sweeping processes Godoy, Matías Torres-Valdebenito, Manuel Vilches, Emilio Optimization and Control Dynamical Systems 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. |
| title | A fixed-point approach to history-dependent sweeping processes |
| topic | Optimization and Control Dynamical Systems |
| url | https://arxiv.org/abs/2412.19210 |