A MATHEMATICAL MODEL OF STRING OSCILLATIONS WITH NONLINEAR CONDITION
In the present paper we investigate the initial-boundary value problems describing oscillation processes with a nonlinear condition. This kind of problems arises in a simulation of string oscillations, where the movement is restricted by a sleeve concentrated at one point. We consider the cases when the sleeve is located at the end of a segment and at the node of a graph-star. The main purpose of the research is to obtain an explicit form of external influences, allowing to put the process of oscillations from the initial state to the final state for a small period of time. Analogues of the d’Alembert formula are obtained. Some control problems are analyzed and explicit forms of control functions are presented.