Note on the Barenblatt Power Series Solution to the Boussinesq Equation

SONG Zhi-yao; LI Ling; David Lockington

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SONG Zhi-yao, LI Ling, David Lockington. Note on the Barenblatt Power Series Solution to the Boussinesq Equation[J]. Applied Mathematics and Mechanics, 2007, 28(6): 735-740.

Citation:

SONG Zhi-yao, LI Ling, David Lockington. Note on the Barenblatt Power Series Solution to the Boussinesq Equation[J]. Applied Mathematics and Mechanics, 2007, 28(6): 735-740.

Citation:

SONG Zhi-yao, LI Ling, David Lockington. Note on the Barenblatt Power Series Solution to the Boussinesq Equation[J]. Applied Mathematics and Mechanics, 2007, 28(6): 735-740.

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Note on the Barenblatt Power Series Solution to the Boussinesq Equation

1.
State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Ocean College, Hohai University, Nanjing 210098, P. R. China;

Received Date: 2006-10-30
Rev Recd Date: 2007-03-05
Publish Date: 2007-06-15

Abstract

Abstract

A self-similar analytical solution of the Boussinesq equation of groundwater flow in a semi-infinite porous medium when the hydraulic head at the boundary behaves like a power of time was presented(Barenblatt (1952) obtained a power series solution,but he listed only the first three coefficients and did not give the recurrent formula among the coefficients.A formal proof of convergence of the series did not appear).The recurrent formula for the coefficients was obtained using the method of power series expansion,and the convergence of the series was proven.The results can be easily understood and used by engineers in catchment hydrology and baseflow studies as well as agricultural drainage problems.
- power series expansion,
- similarity solution,
- recurrent formula,
- convergence

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References(6)

References

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