Geodesic
On a~degenerate boundary value problem for the porous medium equation in spherical coordinates
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 1, pp. 119-129

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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.
Keywords: porous medium equation, boundary value problem, analytical solution, boundary element method. 
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     title = {On a~degenerate boundary value problem for the porous medium equation in spherical coordinates},
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A. L. Kazakov; P. A. Kuznetsov; L. F. Spevak. On a~degenerate boundary value problem for the porous medium equation in spherical coordinates. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 1, pp. 119-129. http://geodesic.mathdoc.fr/item/TIMM_2014_20_1_a11/