Smoothness of Solutions to the Damping Problem for Nonstationary Control System with Delay of Neutral Type on the Whole Interval

We consider the damping problem for a nonstationary control system described by a system of differential-difference equations of neutral type with smooth matrix coefficients and several delays. This problem is equivalent to the boundary-value problem for a system of second-order differential-differe...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2024, Vol.283 (2), p.167-182
Main Author: Adkhamova, A. Sh
Format: Article
Language:English
Subjects:
Boundary value problems
Control systems
Damping
Difference equations
Differential equations
Mathematics
Mathematics and Statistics
Smoothness
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Summary:We consider the damping problem for a nonstationary control system described by a system of differential-difference equations of neutral type with smooth matrix coefficients and several delays. This problem is equivalent to the boundary-value problem for a system of second-order differential-difference equations, which has a unique generalized solution. It is proved that the smoothness of this solution can be violated on the considered interval and is preserved only on some subintervals. Sufficient conditions for the initial function are obtained to ensure the smoothness of the generalized solution over the entire interval.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-024-07247-1