Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2019, Volume 160, Pages 74–84 (Mi into426)  
This article is cited in 1 scientific paper (total in 1 paper)

Boundary displacement control for the oscillation process with boundary conditions of damping type for a time less than critical

E. I. Moiseevab, A. A. Kholomeyevaa, A. A. Frolovba

a Lomonosov Moscow State University
b Federal Research Center "Computer Science and Control" of Russian Academy of Sciences, Moscow
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Abstract: In this paper, we study the problem of boundary control of string oscillations, which is carried out over a period of time less than the critical time. The control is performed by a displacement of one end of the string, whereas at the other end a uniform boundary condition with oblique derivative is given, and the direction of this derivative does not coincide with characteristics. The classical statement of the problem is considered. Necessary and sufficient conditions for the existence of a unique control are found and the control itself is obtained in an explicit analytical form.
Keywords: wave equation, displacement control, time less than critical, boundary conditions with oblique derivative.
Funding agency Grant number
Russian Science Foundation 16-11-10194
This work was supported by the Russian Foundation for Basic Research (project No. 16-11-10194).
Bibliographic databases:
Document Type: Article
UDC: 517.95
MSC: 35L05
Language: Russian
Citation: E. I. Moiseev, A. A. Kholomeyeva, A. A. Frolov, “Boundary displacement control for the oscillation process with boundary conditions of damping type for a time less than critical”, Proceedings of the International Conference on Mathematical Modelling in Applied Sciences ICMMAS-17, St. Petersburg Polytechnic University, July 24-28, 2017, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 160, VINITI, Moscow, 2019, 74–84
Citation in format AMSBIB
\Bibitem{MoiKhoFro19}
\by E.~I.~Moiseev, A.~A.~Kholomeyeva, A.~A.~Frolov
\paper Boundary displacement control for the oscillation process with boundary conditions of damping type for a time less than critical
\inbook Proceedings of the International Conference on Mathematical Modelling in Applied Sciences ICMMAS-17,
St. Petersburg Polytechnic University, July 24-28, 2017
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2019
\vol 160
\pages 74--84
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into426}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3981832}
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