BV Solutions to Evolution Inclusion with a Time and Space Dependent Maximal Monotone Operator-Reference-Cited by-同舟云学术

BV Solutions to Evolution Inclusion with a Time and Space Dependent Maximal Monotone Operator

Published:2024-03-18 Issue:6 Volume:12 Page:896
ISSN:2227-7390
Container-title:Mathematics
language:en
Short-container-title:Mathematics

Author:

Castaing Charles¹,Godet-Thobie Christiane²^ORCID,Monteiro Marques Manuel D. P.³

Affiliation:

1. Institut Montpelliérian Alexander Grothendieck, Université de Montpellier II, CEDEX 5, 34095 Montpellier, France

2. Laboratoire de Mathématiques de Bretagne Atlantique, Université de Brest, CNRS, UMR 6205, 6, Avenue Victor Le Gorgeu, CS 9387, CEDEX 3, 29238 Brest, France

3. CMAFc10, Departemento de Matematica, Faculdade de Ciencias de Lisboa, Campo Grande, 1749-016 Lisboa, Portugal

Abstract

This paper deals with the research of solutions of bounded variation (BV) to evolution inclusion coupled with a time and state dependent maximal monotone operator. Different problems are studied: existence of solutions, unicity of the solution, existence of periodic and bounded variation right continuous (BVRC) solutions. Second-order evolution inclusions and fractional (Caputo and Riemann–Liouville) differential inclusions are also considered. A result of the Skorohod problem driven by a time- and space-dependent operator under rough signal and a Volterra integral perturbation in the BRC setting is given. The paper finishes with some results for fractional differential inclusions under rough signals and Young integrals. Many of the given results are novel.

Publisher

MDPI AG

Link

https://www.mdpi.com/2227-7390/12/6/896/pdf

Reference63 articles.

1. Castaing, C., Marie, N., and Raynaud de Fitte, P. (2018). Sweeping Process Perturbed by Rough Signal, Springer International Publishing.

2. A Skorohod problem governed by a closed convex moving set;Castaing;J. Convex Anal.,2016

3. Deterministic and stochastic differential equations in Hilbert Spaces involving multivalued maximal monotone operators;Rascanu;Panamer. Math. J.,1996

4. Cadlag Skorohod problem driven by Maximal monotone operator;Maticiuc;JMAA,2015

5. Dynamical Systems Coupled with Monotone Set-Valued Operators: Formalisms, Applications, Well-Posedness and Stability;Brogliato;SIAM Rev.,2020