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Laplace transform inversion for late‐time behavior of groundwater flow problems
Author(s) -
Mathias Simon A.,
Zimmerman Robert W.
Publication year - 2003
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/2003wr002246
Subject(s) - laplace transform , mathematics , mathematical analysis , laplace transform applied to differential equations , inversion (geology) , fourier transform , coefficient matrix , groundwater , inverse laplace transform , matrix (chemical analysis) , groundwater flow equation , mellin transform , groundwater flow , geology , geotechnical engineering , materials science , physics , aquifer , geomorphology , eigenvalues and eigenvectors , structural basin , quantum mechanics , composite material
Laplace transforms are widely used in solving groundwater flow problems. In the groundwater literature, it has frequently been asserted or assumed that the late‐time behavior is governed by the behavior of the Laplace transform for small values of the Laplace variable. Careful reading of authoritative monographs on Laplace transforms shows that this correspondence does not generally hold. In this article the proper asymptotic formula is reviewed and is applied to the problem of water influx into a slab‐like matrix block in a dual‐porosity medium. In doing so, we clear up a long‐standing discrepancy between the fracture/matrix transfer coefficient that has been calculated by Laplace methods and the coefficient which has been found by applying Fourier methods in the time domain.