Modeling of unsteady elastic diffusion processes in a hollow cylinder taking into account the diffusion fluxes relaxation

A one-dimensional problem of elastic diffusion for a hollow orthotropic multicomponent cylinder under the action of external pressure, which is uniformly distributed over its inner and outer surfaces is considered. The mathematical model includes a system of equations of elastic diffusion in a cylindrical coordinate system, which takes into account relaxation diffusion effects, implying finite propagation velocities of diffusion processes. The problem is solved by the method of equivalent boundary conditions, according to which auxiliary problem is considered, the solution of which is obtained by expanding into series in terms of eigenfunctions of the elastic-diffusion operator. Further, the relations that connects the right parts of the boundary conditions of both problems is constructed. This relations represents a system integral equation. Its solution is sought using quadrature formulas. A calculation example for a three-component hollow cylinder is considered.