Geodesic
On the wave equation with the hysteresis type condition
Vestnik rossijskih universitetov. Matematika, Tome 23 (2018) no. 122, pp. 235-242

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In this paper we investigate the initial-boundary value problem describing the oscillation process with a hysteresis-type boundary condition. This kind of problem arises in modeling of the string oscillations, where the movement is restricted by a sleeve concentrated at one point $x=l.$ We suppose that the string is located along the segment $[0,l]$ and the sleeve can move in perpendicular to $ [0, l] $ direction. The analog of d'Alembert formula is obtained. A boundary control problem is analyzed for a small period of time. The boundary control problem is to find a control function allowing to put the oscillation process from the initial state to the given final state.
Keywords: wave equation, string oscillations, boundary control problem.
Mots-clés : d’Alembert formula 
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     title = {On the wave equation with the hysteresis type condition},
     journal = {Vestnik rossijskih universitetov. Matematika},
     pages = {235--242},
     publisher = {mathdoc},
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     year = {2018},
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     url = {http://geodesic.mathdoc.fr/item/VTAMU_2018_23_122_a14/}
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N. I. Voskovskaya; M. B. Zvereva; M. I. Kamenskii. On the wave equation with the hysteresis type condition. Vestnik rossijskih universitetov. Matematika, Tome 23 (2018) no. 122, pp. 235-242. http://geodesic.mathdoc.fr/item/VTAMU_2018_23_122_a14/