Note on Barenblatt power series solution to Boussinesq equation

Song, Z.Y., Li, L. and Lockington, D.A. (2007) Note on Barenblatt power series solution to Boussinesq equation. Applied Mathematics And Mechanics-english Edition, 28 6: 823-828. doi:10.1007/s10483-007-0612-x


Author Song, Z.Y.
Li, L.
Lockington, D.A.
Title Note on Barenblatt power series solution to Boussinesq equation
Journal name Applied Mathematics And Mechanics-english Edition   Check publisher's open access policy
ISSN 0253-4827
Publication date 2007-01-01
Year available 2007
Sub-type Article (original research)
DOI 10.1007/s10483-007-0612-x
Open Access Status Not yet assessed
Volume 28
Issue 6
Start page 823
End page 828
Total pages 6
Place of publication Shanghai
Publisher Shanghai Univ
Language eng
Subject 291100 Environmental Engineering
260500 Hydrology
770000 - Environmental Management
C1
Abstract To the self-similar analytical solution of the Boussinesq equation of groundwater flow in a semi-infinite porous medium, when the hydraulic head at the boundary behaved like a power of time, Barenblatt obtained a power series solution. However, 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 in his works. In this paper, the recurrent formula for the coefficients is obtained by using the method of power series expansion, and the convergence of the series is proven. The results can be easily understood and used by engineers in the catchment hydrology and baseflow studies as well as to solve agricultural drainage problems.
Keyword Mathematics, Applied
Mechanics
power series expansion
similarity solution
recurrent formula
convergence
Groundwater
Flow
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

 
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Created: Tue, 19 Feb 2008, 00:13:21 EST