TY  - JOUR
ID  - Răsvan2022
LB  - Răsvan2022
AU  - Răsvan, Vladimir
TI  - Critical cases in neutral functional differential equations, arising from hydraulic engineering
ST  - Critical cases in neutral functional differential equations, arising from hydraulic engineering
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2022
VL  - 42
IS  - 4
SP  - 605
EP  - 633
DO  - https://doi.org/10.7494/OpMath.2022.42.4.605
UR  - https://doi.org/10.7494/OpMath.2022.42.4.605
AB  - 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.
KW  - \(1D\) hyperbolic partial differential equations
KW  - neutral functional differential equations
KW  - difference operator
KW  - critical case
SN  - 1232-9274
ER  -