Quasistationary nonlinear problem of thermal conduction with spherical symmetry in the region with a free boundary

The article discusses a boundary value single-phase problem with a free boundary for a quasistationary nonlinear inhomogeneous heat conduction equation with a spherically symmetric thermal field. The domain of the problem is degenerated at the initial moment of time. To find a free boundary, the problem is supplemented by Stefan’s condition. It is assumed that thermal conductivity and latent heat of melting depend on temperature. The study of the boundary value problem was carried out by transforming it to an equivalent system of integral equations, for which a proof of solvability and uniqueness of the solution was obtained. An iterative algorithm for the numerical solution of a system of integral equations has been developed. The results of a computational experiment on the analytical solution of a boundary value problem have been presented.