Abstract:
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.
Citation:
A. Sh. Adkhamova, “Smoothness of solutions to the damping problem for nonstationary control system with delay”, Science — Technology — Education — Mathematics — Medicine, CMFD, 68, no. 1, PFUR, M., 2022, 14–24
\Bibitem{Adk22}
\by A.~Sh.~Adkhamova
\paper Smoothness of solutions to the damping problem for nonstationary control system with delay
\inbook Science — Technology — Education — Mathematics — Medicine
\serial CMFD
\yr 2022
\vol 68
\issue 1
\pages 14--24
\publ PFUR
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd449}
\crossref{https://doi.org/10.22363/2413-3639-2022-68-1-14-24}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4422554}
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https://www.mathnet.ru/eng/cmfd449
https://www.mathnet.ru/eng/cmfd/v68/i1/p14
This publication is cited in the following 2 articles:
A. Sh. Adkhamova, A. L. Skubachevskii, “Zadacha ob uspokoenii sistemy upravleniya s posledeistviem s razlichnym chislom vkhodov i vykhodov”, Funktsionalnye prostranstva. Differentsialnye operatory. Problemy
matematicheskogo obrazovaniya, SMFN, 70, no. 2, Rossiiskii universitet druzhby narodov, M., 2024, 189–200
A. Sh. Adkhamova, “Gladkost reshenii zadachi ob uspokoenii nestatsionarnoi sistemy upravleniya s posledeistviem neitralnogo tipa na vsem intervale”, SMFN, 69, no. 1, Rossiiskii universitet druzhby narodov, M., 2023, 1–17
Citation in format AMSBIB
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