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On the wave equation with the hysteresis type condition


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.


wave equation; string oscillations; d’Alembert formula; boundary control problem

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