An analytical and numerical study of a nonlinear parabolic equation with degeneration for the cases of circular and spherical symmetry

• For the porous medium equation, the existence and uniqueness theorem is proved.
• Analytical solution is constructed in the form of a converged multiple power series.
• Solution algorithms based on the boundary element method are proposed.
• As the order increases, the truncated series approaches the BEM solution.

The paper deals with a nonlinear parabolic equation describing the processes of diffusion, filtration and heat conduction for the cases of the central symmetry of the problems. For the nonzero boundary conditions specified on moving manifold, the existence and uniqueness theorem is formulated and proved, which is analogous to the Cauchy–Kovalevskaya theorem in the case under study, and the analytical solution is constructed in the form of a multiple power series. Solution algorithms based on the boundary element method are proposed. Illustrating examples are discussed.