Abstract:
An analytical method for solving the wave equation describing the oscillations of systems with moving boundaries is considered.
By replacing variables that set boundaries and leave the equation invariant, the original boundary value problem is reduced to a system of functional – difference equations that can be solved using forward and reverse methods. The inverse method is described, which allows us to apply sufficiently diverse laws of boundary motion to the laws obtained from the solution of the inverse problem. New partial solutions for a fairly wide range of boundary motion laws are obtained. A direct asymptotic method for approximating the solution of a functional equation is considered. The errors of the approximate method are estimated depending on the speed of the border movement.

Keywords:wave equation, boundary value problems, oscillation of system with moving boundarie, substitution of variables, law of boundary motion, functional equation.