TY - JOUR
T1 - Approximate Similarity Solution to a Nonlinear Diffusion Equation with Spherical Symmetry
AU - Mortensen , J.
AU - Olsen , S.
AU - Parlange , J.-Y.
AU - Telyakovskly , A. S.
JO - International Journal of Numerical Analysis and Modeling
VL - 1
SP - 105
EP - 114
PY - 2012
DA - 2012/09
SN - 9
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/614.html
KW - Approximate solutions, similarity solutions, Boussinesq equation, nonlinear diffusion.
AB - <p style="text-align: justify;">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 Li et al. [8] 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.</p>