Critical cases in neutral functional differential equations, arising from hydraulic engineering

• Autorzy: Răsvan Vladimir

Identyfikatory

DOI

10.7494/OpMath.2022.42.4.605

• Języki publikacji: EN

Abstrakty

EN

This paper starts from several applications described by initial/boundary value problems for 1D (time and one space variable) hyperbolic partial differential equations whose basic properties and stability of equilibria are studied throughout the same properties for certain associated neutral functional differential equations. It is a common fact that asymptotic stability for neutral functional differential equations is normally obtained under the assumption of asymptotic stability of the difference operator associated to the aforementioned neutral functional differential equations. However the physically meaningful applications presented in the paper have the associated difference operator(s) in critical cases (their stability is, generally speaking, non-asymptotic). Consequently the stability of the considered application models is either non-asymptotic or fragile (in a sense introduced in the paper). The models represent an overview gathered from various fields, processed here in order to emphasize the associated neutral functional differential equations which, consequently, are a challenge to the usual approaches. In the concluding part there are suggested possible ways to overcome these difficulties.

Słowa kluczowe

EN

1D hyperbolic partial differential equations; neutral functional differential equation; difference operator; critical case; differential equations

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2022
• Tom: Vol. 42, no. 4
• Strony: 605--633
• Opis fizyczny: Bibliogr. 52 poz., rys.

Twórcy

autor

Răsvan Vladimir

• University of Craiova, Department of Automatic Control and Electronics, 13 A. I. Cuza Street, Craiova, RO-200585 Romania
• Romanian Academy of Engineering Sciences ASTR, 26 Dacia Blvd, Bucharest, RO-010413 Romania

• https://orcid.org/0000-0002-4569-9543

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Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).