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Approximate similarity solution to a nonlinear diffusion equation with spherical symmetry. (English) Zbl 1329.76322

Summary: In this article we construct an approximate similarity solution to a nonlinear diffusion equation in spherical coordinates. In hydrology this equation is known as the Boussinesq equation when written in planar or cylindrical coordinates. Recently, L. Li et al. [“Similarity solution of axisymmetric flow in porous media.” Adv. Water Resourc. 28, 1076–1082 (2005)] obtained an approximate similarity solution to the Boussinesq equation in cylindrical coordinates. Here we consider the same problem in spherical coordinates with the prescribed power law point source boundary condition. The resulting scaling function has a power law singularity at the origin versus a logarithmic singularity in the cylindrical case.

MSC:

76R50 Diffusion
34A45 Theoretical approximation of solutions to ordinary differential equations
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