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Volume 9, Issue 1
Approximate Similarity Solution to a Nonlinear Diffusion Equation with Spherical Symmetry

J. Mortensen, S. Olsen, J.-Y. Parlange & A. S. Telyakovskly

Int. J. Numer. Anal. Mod., 9 (2012), pp. 105-114.

Published online: 2012-09

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  • Abstract

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.

  • Keywords

Approximate solutions, similarity solutions, Boussinesq equation, nonlinear diffusion.

  • AMS Subject Headings

34B15, 35K20, 76S05, 80A20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-9-105, author = {Mortensen , J.Olsen , S.Parlange , J.-Y. and Telyakovskly , A. S.}, title = {Approximate Similarity Solution to a Nonlinear Diffusion Equation with Spherical Symmetry}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2012}, volume = {9}, number = {1}, pages = {105--114}, abstract = {

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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/614.html} }
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 -

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.

Mortensen , J.Olsen , S.Parlange , J.-Y. and Telyakovskly , A. S.. (2012). Approximate Similarity Solution to a Nonlinear Diffusion Equation with Spherical Symmetry. International Journal of Numerical Analysis and Modeling. 9 (1). 105-114. doi:
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