Modeling of Oscillatory Processes with Fading Effect and Their Accurate Description
The initial boundary value problem for the hyperbolic equation of the second order with nontrivial boundary condition is discussed in the paper. This problem is a mathematical model of different oscillatory processes. Thus, for example, the model of voltage distribution in a telegraph line emerges for the one-dimensional equation of oscillations. The models of oscillations of a round homogeneous solid membrane and membrane with an opening, and the model of gas oscillations in the sphere and spherical region emerge for two- and three-dimensional operators, but taking into account the radial symmetry of oscillations. The unified algorithm for reducing the corresponding problems to the initial boundary value problem with trivial boundary conditions is proposed. The description of solution development in the form of Fourier series by eigen functions of the corresponding Sturm-Liouville problem is presented.