Geodesic
Smoothness of solutions to the damping problem for nonstationary control system with delay of neutral type on the whole interval
Contemporary Mathematics. Fundamental Directions, Contemporary Mathematics. Fundamental Directions, Tome 69 (2023) no. 1, pp. 1-17.

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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.
Keywords: neutral-type differential-difference equation, damping problem for control system with aftereffect, Krasovskii problem, generalized solution, smoothness of solution. 
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A. S. Adkhamova. Smoothness of solutions to the damping problem for nonstationary control system with delay of neutral type on the whole interval. Contemporary Mathematics. Fundamental Directions, Contemporary Mathematics. Fundamental Directions, Tome 69 (2023) no. 1, pp. 1-17. http://geodesic.mathdoc.fr/item/CMFD_2023_69_1_a0/

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