INTEGRATION OF INITIAL BOUNDARY VALUE PROBLEMS WITH FREE AND MOVING BOUNDARIES

Nowadays the study of initial boundary value problems with variable boundary is relevant both in Russia and abroad: they describe the phenomena of melting and solidification, oscillating and diffusion phenomena, they are used in financial mathematics etc. A brief overview of these problems and methods of their solution is given in monograph [4]. In this paper, the method of asymptotic integration is used for solving the equations of hyperbolic type, when the moving boundary is considered to be a known function of time. In our work, a small parameter characterizes the rate of the boundary growth. A comparison of the results of the asymptotic and numerical integration of the problem of longitudinal vibrations of the rigid body on a rope of variable length is carried out