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The Markov power moment problem in problems of controllability and frequency extinguishing for the wave equation on a half-axis |
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| Authors: | G.M. Sklyar L.V. Fardigola |
| Affiliation: | a Institute of Mathematics, Szczecin University, 15, Wielkopolska Str., 70451 Szczecin, Poland b Department of Mathematical Analysis, Kharkov National University, 4, Liberty Sqr., 61077 Kharkov, Ukraine c Mathematical Division, Institute for Low Temperature Physics of the National Academy of Sciences of Ukraine, 47, Lenin Ave., 61103 Kharkov, Ukraine |
| Abstract: | In this paper necessary and sufficient conditions of null-controllability and approximate null-controllability are obtained for the wave equation on a half-axis. Controls solving these problems are found explicitly. Moreover, bang-bang controls solving the approximate null-controllability problem are constructed with the aid of solutions of a frequency extinguishing problem in the restricted band (−a,a) for this equation and the Markov power moment problem. |
| Keywords: | Wave equation Half-axis Controllability problem Moment problem Frequency extinguishing problem |
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