On a degenerate boundary value problem for the porous medium equation in spherical coordinates

We study a degenerate boundary value problem for the porous medium equation in the case of spherical coordinates. The results of this study can be applied to the problem of heat propagation in a neighborhood of a closed spherical surface. For the boundary value problem, we prove the existence and uniqueness theorem for solutions in the class of analytical functions and propose a numerical method for constructing solutions based on the boundary element approach. We use both truncated series and the proposed numerical method to carry out sample computations.