Modeling of elastic diffusion processes in a hollow cylinder under the action of unsteady volume perturbations

A one-dimensional initial-boundary value problem for a hollow orthotropic multicomponent cylinder under the action of volumetric elastic diffusion perturbations 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 flows.
The problem is solved by the method of equivalent boundary conditions. To do this, we consider some auxiliary problem, the solution of which can be obtained by expanding into series in terms of eigenfunctions of the elastic diffusion operator. Next, we construct relations that connect the right-hand sides of the boundary conditions of both problems, which are a system of Volterra integral equations of the first kind. A calculation example for a three-component hollow cylinder is considered.