Galerkin-like Method for Integro-Differential Inclusions with applications to Volterra Sweeping processes

Fuente: arXiv
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Autores principales: Pérez-Aros, Pedro, Torres-Valdebenito, Manuel, Vilches, Emilio
Formato: Preprint
Publicado: 2023
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author Pérez-Aros, Pedro
Torres-Valdebenito, Manuel
Vilches, Emilio
author_facet Pérez-Aros, Pedro
Torres-Valdebenito, Manuel
Vilches, Emilio
contents In this paper, we develop the Galerkin-like method to address first-order integro-differential inclusions. Under compactness or monotonicity conditions, we obtain new results for the existence of solutions for this class of problems, which generalize existing results in the literature and provide new insights for differential inclusions with an unbounded right-hand side. The effectiveness of the proposed approach is illustrated by presenting new existence results for nonconvex state-dependent Volterra sweeping processes, where the right-hand side is unbounded, and the classical theory of differential inclusions is not applicable. This is the first result of its kind. The paper concludes with an application to the existence of an optimal control problem governed by nonconvex state-dependent Volterra sweeping processes in finite dimensions.
format Preprint
id arxiv_https___arxiv_org_abs_2306_07821
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Galerkin-like Method for Integro-Differential Inclusions with applications to Volterra Sweeping processes
Pérez-Aros, Pedro
Torres-Valdebenito, Manuel
Vilches, Emilio
Optimization and Control
34A60, 49J52, 34G25, 49J53
In this paper, we develop the Galerkin-like method to address first-order integro-differential inclusions. Under compactness or monotonicity conditions, we obtain new results for the existence of solutions for this class of problems, which generalize existing results in the literature and provide new insights for differential inclusions with an unbounded right-hand side. The effectiveness of the proposed approach is illustrated by presenting new existence results for nonconvex state-dependent Volterra sweeping processes, where the right-hand side is unbounded, and the classical theory of differential inclusions is not applicable. This is the first result of its kind. The paper concludes with an application to the existence of an optimal control problem governed by nonconvex state-dependent Volterra sweeping processes in finite dimensions.
title Galerkin-like Method for Integro-Differential Inclusions with applications to Volterra Sweeping processes
topic Optimization and Control
34A60, 49J52, 34G25, 49J53
url https://arxiv.org/abs/2306.07821