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

Castaing, Charles; Godet-Thobie, Christiane; Monteiro Marques, Manuel D. P.

doi:10.3390/math12060896

Open AccessArticle

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

by

Charles Castaing

^1,*,

Christiane Godet-Thobie

^2,*

and

Manuel D. P. Monteiro Marques

³

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

^*

Authors to whom correspondence should be addressed.

Mathematics 2024, 12(6), 896; https://doi.org/10.3390/math12060896

Submission received: 9 January 2024 / Revised: 8 March 2024 / Accepted: 14 March 2024 / Published: 18 March 2024

(This article belongs to the Special Issue Set-Valued Analysis, 3rd Edition)

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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.

Keywords: bounded variation; differential inclusion; maximal monotone operator; pseudo-distance; right continuous; second order; fractional derivative; fixed point

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MDPI and ACS Style

Castaing, C.; Godet-Thobie, C.; Monteiro Marques, M.D.P. BV Solutions to Evolution Inclusion with a Time and Space Dependent Maximal Monotone Operator. Mathematics 2024, 12, 896. https://doi.org/10.3390/math12060896

AMA Style

Castaing C, Godet-Thobie C, Monteiro Marques MDP. BV Solutions to Evolution Inclusion with a Time and Space Dependent Maximal Monotone Operator. Mathematics. 2024; 12(6):896. https://doi.org/10.3390/math12060896

Chicago/Turabian Style

Castaing, Charles, Christiane Godet-Thobie, and Manuel D. P. Monteiro Marques. 2024. "BV Solutions to Evolution Inclusion with a Time and Space Dependent Maximal Monotone Operator" Mathematics 12, no. 6: 896. https://doi.org/10.3390/math12060896

APA Style

Castaing, C., Godet-Thobie, C., & Monteiro Marques, M. D. P. (2024). BV Solutions to Evolution Inclusion with a Time and Space Dependent Maximal Monotone Operator. Mathematics, 12(6), 896. https://doi.org/10.3390/math12060896

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

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

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