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Articles

Reconstruction of unknown storativity and transmissivity functions in 2D groundwater equations

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Pages 1796-1816 | Received 15 May 2019, Accepted 22 Apr 2020, Published online: 02 Jun 2020

References

  • Meier PM, Carrera J, Sanchez-Villa X. A numerical study on the relationship between transmissivity and specific capacity in heterogeneous aquifers. Groundwater. 1999;37(4):611–617. doi: 10.1111/j.1745-6584.1999.tb01149.x
  • Todd DK. Groundwater hydrology. 2nd ed. New-York: John Wiley; 2004.
  • Bulter J. Pumping tests for aquifer evaluation, time for change? Groundwater. 2009;46:615–617.
  • Hoeksema RJ, Kitanidis PK. An application of the geostatistical approach to the inverse problem in two-dimensional groundwater modeling. Water Resour Res. 1984;20:1003–1020. doi: 10.1029/WR020i007p01003
  • Yeh TJ, Lee C. Time to change the way we collect and analyze data for aquifer characterization. Groundwater. 2007;45:116–118. doi: 10.1111/j.1745-6584.2006.00292.x
  • Sterrett RJ. Groundwater and wells. 3rd ed. New Brighton, Minnesota: Johnson Screens; 2007.
  • Theis CV. The relation between the lowering of the piezometric surface and the rate and duration of discharge of a well using groundwater storage. Am Geophys Union Trans. 1935;16:519–524. doi: 10.1029/TR016i002p00519
  • Cooper HH, Jacob CE. A generalized graphical method for evaluating formation constants and summarizing well-field history. Am Geophys Union Trans. 1946;27(4):526–534. doi: 10.1029/TR027i004p00526
  • Jim Yeh TC. Stochastic modelling of groundwater flow and solute transport in aquifers. Hydrlog Process. 1992;6:369–395. doi: 10.1002/hyp.3360060402
  • Abdel-Aziz H, Abdel-Gawad A, El-Hadi HA. Parameter estimation of pumping test data using genetic algorithm. In: Thirteenth International Water Technology Conference, IWTC 13; Hurghada-Egypt. 2009.
  • Beckie R, Harvey CF. What does a slug test measure: an investigation of instrument response and the effects of heterogeneity. Water Resour Res. 2002;38(12):1–14. doi: 10.1029/2001WR001072
  • Castagna M, Bellin A. A Bayesianapproach for inversion of hydraulic tomographic data. Water Resour Res. 2009;45:W04410. doi:10.1029/2008WR007078
  • Cleveland TG. Type-curve matching using a computer spreadsheet. Groundwater. 1996;34(3):554–562. doi: 10.1111/j.1745-6584.1996.tb02038.x
  • Shapoori V, Peterson TJ, Western AW, et al. Estimating aquifer properties using groundwater hydrograph modelling. Hydrol Process. 2015;29(26):5424–5437. doi:10.1002/hyp.10583
  • Nelson RW. In-place measurement of permeability in heterogeneous media: experimental and computational considerations. J Geophys Res. 1960;66:2469–2478. doi: 10.1029/JZ066i008p02469
  • Richter GR. An inverse problem for the steady state diffusion equation. SIAM J Math Anal. 1981;41:210–221. doi: 10.1137/0141016
  • Rogelio VG, Mauro G, Giansilvio P, et al. The differential system method for the identification of transmissivity and storativity. Transport Porous Media. 1997;26:339–371. doi: 10.1023/A:1006568818150
  • Anderson MP, Woessner WW. Applied groundwater modeling. San Diego, CA: Academic Press, Inc.; 1992.
  • Bear J. Hydraulics of groundwater. New York: McGraw-Hill; 1979.
  • Lions JL. Pointwise control for distributed systems in control and estimation in distributed parameters systems, Edited by Banks H.T. SIAM. 1992.
  • Schwartz L. Théorie des distributions. Paris: Hermann; 1966.
  • Berestycki H, Hamel F, Nadirashvili N. Elliptic eigenvalue problems with large drift and applications to nonlinear propagation phenomena. Commun Math Phys. 2005;253:451–480. doi: 10.1007/s00220-004-1201-9
  • Chen XF, Lou Y. Principal eigenvalue and eigenfunction of an elliptic operator with large advection and its application to a competition model. Indiana Univ Math J. 2008;57:627–658. doi: 10.1512/iumj.2008.57.3204
  • El Jai A, Pritchard G. Capteurs et Actionneurs dans l'Analyse des systèmes distribués (RMA 3). Paris: Masson; 1986.
  • El Badia A, Ha Duong T. On an inverse source problem for the heat equation: application to a pollution detection problem. J Inverse Ill-Posed Probl. 2002;10:585–599. doi: 10.1515/jiip.2002.10.6.585
  • Hamdi A. Detection and identification of multiple unknown time-dependent point sources occurring in 1D evolutionj transport equations. Inverse Probl Sci Eng. 2016;25(4):532–554. doi: 10.1080/17415977.2016.1172224
  • Barles G, Blanc A-P, Georgelin C, et al. Remarks on the maximum principle for nonlinear elliptic PDEs with quadratic growth conditions. Ann Scuola Norm Sup Pisa Cl Sci. 1999;28(4):381–404.
  • Titchmarsh EC. Introducton to the theory of Fourier integrals. Oxford: Oxford University Press; 1939.
  • Alarcon S, Garcia-Mellian J, Quaas A. Keller-Osserman type conditions for some elliptic problems with gradient terms. J Differ Equ. 2012;252(2):886–914. doi: 10.1016/j.jde.2011.09.033

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