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Volumn 9, Issue 2, 2009, Pages 111-135

A quasi-boundary semi-analytical method for backward In time advection-dispersion equation

Author keywords

Advection dispersion equation; Fredholm integral equation; Groundwater contaminant distribution; Inverse problem; Two point boundary value prob lem

Indexed keywords

ADVECTION- DISPERSION EQUATION; ANALYTICAL METHOD; CONCENTRATION FIELDS; ERROR ESTIMATES; FOURIER-SERIES EXPANSION; FREDHOLM INTEGRAL EQUATION; GROUNDWATER CONTAMINANT DISTRIBUTION; KERNEL FUNCTION; NEW APPROACHES; NUMERICAL EXAMPLE; SECOND KIND FREDHOLM INTEGRAL EQUATION; SEMI-ANALYTICAL METHODS; SPATIAL DISTRIBUTION; TWO-POINT BOUNDARY VALUE PROB- LEM; UNIFORM CONVERGENCE;

EID: 67049088374     PISSN: 15462218     EISSN: 15462226     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (12)

References (30)
  • 1
    • 0031260782 scopus 로고    scopus 로고
    • Continuous dependence on modeling for related Cauchy problems of a class of evolution equations
    • Ames, K. A.; Cobb, S. S. (1997) : Continuous dependence on modeling for related Cauchy problems of a class of evolution equations. J. Math. Anal. Appl., vol. 215, pp. 15-31.
    • (1997) J. Math. Anal. Appl , vol.215 , pp. 15-31
    • Ames, K.A.1    Cobb, S.S.2
  • 2
    • 1942417404 scopus 로고    scopus 로고
    • Continuous dependence on modeling for some well-posed perturbations of the backward heat equation
    • Ames, K. A.; Payne, L. E. (1999) : Continuous dependence on modeling for some well-posed perturbations of the backward heat equation. J. Inequal. Appl., vol. 3, pp. 51-64.
    • (1999) J. Inequal. Appl , vol.3 , pp. 51-64
    • Ames, K.A.1    Payne, L.E.2
  • 3
    • 67049120679 scopus 로고    scopus 로고
    • Atmadja, J. (2001) : The marching-jury backward beam equation method and its application to backtracking non-reactive plumes in groundwater. Ph. D. Disserta- tion, Columbia University, New York.
    • Atmadja, J. (2001) : The marching-jury backward beam equation method and its application to backtracking non-reactive plumes in groundwater. Ph. D. Disserta- tion, Columbia University, New York.
  • 4
    • 0035653415 scopus 로고    scopus 로고
    • State of the art report on mathematical methods for groundwater pollution source identification
    • Atmadja, J.; Bagtzoglou, A. C. (2001a) : State of the art report on mathematical methods for groundwater pollution source identification. Environ. Forensics, vol. 2, pp. 205-214.
    • (2001) Environ. Forensics , vol.2 , pp. 205-214
    • Atmadja, J.1    Bagtzoglou, A.C.2
  • 5
    • 0034918670 scopus 로고    scopus 로고
    • Pollution source identification in hetero- geneous porous media
    • Atmadja, J.; Bagtzoglou, A. C. (2001b) : Pollution source identification in hetero- geneous porous media. Water Resour. Res, vol. 37, pp. 2113-2125.
    • (2001) Water Resour. Res , vol.37 , pp. 2113-2125
    • Atmadja, J.1    Bagtzoglou, A.C.2
  • 6
    • 17944384926 scopus 로고    scopus 로고
    • Marching-jury backward beam equation and quasi-reversibility methods for hydrologic inversion: Application to contami- nant plume spatial distribution recovery
    • Atmadja, J.; Bagtzoglou, A. C. (2003) : Marching-jury backward beam equation and quasi-reversibility methods for hydrologic inversion: Application to contami- nant plume spatial distribution recovery. Water Resour. Res., vol. 39, pp. 1038-1051.
    • (2003) Water Resour. Res , vol.39 , pp. 1038-1051
    • Atmadja, J.1    Bagtzoglou, A.C.2
  • 7
    • 0004147916 scopus 로고
    • Second Edition, Addison-Wesley, Reading, Massachusetts
    • Apostol, T. M. (1974) : Mathematical Analysis, Second Edition, Addison-Wesley, Reading, Massachusetts.
    • (1974) Mathematical Analysis
    • Apostol, T.M.1
  • 8
    • 33751514577 scopus 로고    scopus 로고
    • Optimal regularization method for ill-posed Cauchy problems
    • Boussetila, N.; Rebbani, F. (2006) : Optimal regularization method for ill-posed Cauchy problems. Electronic J. Diff. Eqns., vol. 2006, pp. 1-15.
    • (2006) Electronic J. Diff. Eqns , vol.2006 , pp. 1-15
    • Boussetila, N.1    Rebbani, F.2
  • 9
    • 33847712471 scopus 로고    scopus 로고
    • A new shooting method for quasi-boundary regularization of backward heat conduction problems
    • Chang, J.-R.; Liu, C.-S.; Chang, C.-W. (2007) : A new shooting method for quasi-boundary regularization of backward heat conduction problems. Int. J. Heat Mass Transfer, vol. 50, pp. 2325-2332.
    • (2007) Int. J. Heat Mass Transfer , vol.50 , pp. 2325-2332
    • Chang, J.-R.1    Liu, C.-S.2    Chang, C.-W.3
  • 10
    • 0007447039 scopus 로고
    • Quasireversibility methods for non- well-posed problems
    • Clark, G. W.; Oppenheimer, S. F. (1994) : Quasireversibility methods for non- well-posed problems. Elect. J. Diff. Eqns., vol. 1994, pp. 1-9.
    • (1994) Elect. J. Diff. Eqns , vol.1994 , pp. 1-9
    • Clark, G.W.1    Oppenheimer, S.F.2
  • 11
    • 10344263455 scopus 로고    scopus 로고
    • A modified quasi-boundary value method for ill-posed problems
    • Denche, M.; Bessila, K. (2005) : A modified quasi-boundary value method for ill-posed problems. J. Math. Anal. Appl., vol. 301, pp. 419-426.
    • (2005) J. Math. Anal. Appl , vol.301 , pp. 419-426
    • Denche, M.1    Bessila, K.2
  • 12
    • 0020767488 scopus 로고
    • Identifying sources of ground- water pollution: An optimization approach
    • Gorelick, S. M.; Evans, B. E.; Remson, I. (1983) Identifying sources of ground- water pollution: An optimization approach. Water Resour. Res., vol. 19, pp. 779-790.
    • (1983) Water Resour. Res , vol.19 , pp. 779-790
    • Gorelick, S.M.1    Evans, B.E.2    Remson, I.3
  • 13
    • 26444607513 scopus 로고    scopus 로고
    • Regularization for a class of ill-posed Cauchy prob- lems
    • Huang, Y.; Zheng, Q. (2005) : Regularization for a class of ill-posed Cauchy prob- lems. Proc. A. M. S., vol. 133, pp. 3005-3012.
    • (2005) Proc. A. M. S , vol.133 , pp. 3005-3012
    • Huang, Y.1    Zheng, Q.2
  • 15
    • 0035480574 scopus 로고    scopus 로고
    • Cone of non-linear dynamical system and group preserving schemes
    • Liu, C.-S. (2001) : Cone of non-linear dynamical system and group preserving schemes. Int. J. Non-Linear Mech, vol. 36, pp. 1047-1068.
    • (2001) Int. J. Non-Linear Mech , vol.36 , pp. 1047-1068
    • Liu, C.-S.1
  • 16
    • 33744980037 scopus 로고    scopus 로고
    • The Lie-group shooting method for nonlinear two-point bound- ary value problems exhibiting multiple solutions
    • Liu, C.-S. (2006) : The Lie-group shooting method for nonlinear two-point bound- ary value problems exhibiting multiple solutions. CMES: Computer Modeling in Engineering and Sciences, vol. 13, pp. 149-163.
    • (2006) CMES: Computer Modeling in Engineering and Sciences , vol.13 , pp. 149-163
    • Liu, C.-S.1
  • 17
    • 34247135763 scopus 로고    scopus 로고
    • Elastic torsion bar with arbitrary cross-section using the Fred- holm integral equations
    • Liu, C.-S. (2007a) : Elastic torsion bar with arbitrary cross-section using the Fred- holm integral equations. CMC: Computers, Materials and Continua, vol. 5, pp. 31-42.
    • (2007) CMC: Computers, Materials and Continua , vol.5 , pp. 31-42
    • Liu, C.-S.1
  • 18
    • 34250180604 scopus 로고    scopus 로고
    • A meshless regularized integral equation method for Laplace equation in arbitrary interior or exterior plane domains
    • Liu, C.-S. (2007b) : A meshless regularized integral equation method for Laplace equation in arbitrary interior or exterior plane domains. CMES: Computer Model- ing in Engineering and Sciences, vol. 19, pp. 99-109.
    • (2007) CMES: Computer Model- ing in Engineering and Sciences , vol.19 , pp. 99-109
    • Liu, C.-S.1
  • 19
    • 34250207387 scopus 로고    scopus 로고
    • A MRIEM for solving the Laplace equation in the doubly- connected domain
    • Liu, C.-S. (2007c) : A MRIEM for solving the Laplace equation in the doubly- connected domain. CMES: Computer Modeling in Engineering and Sciences, vol. 19, pp. 145-161.
    • (2007) CMES: Computer Modeling in Engineering and Sciences , vol.19 , pp. 145-161
    • Liu, C.-S.1
  • 20
    • 67049087093 scopus 로고    scopus 로고
    • Solving the inverse problems of Laplace equation to determine the Robin coefficient/cracks' position inside a disk
    • in press
    • Liu, C.-S. (2009) : Solving the inverse problems of Laplace equation to determine the Robin coefficient/cracks' position inside a disk. CMES: Computer Modeling in Engineering and Sciences, in press.
    • (2009) CMES: Computer Modeling in Engineering and Sciences
    • Liu, C.-S.1
  • 21
    • 73449138290 scopus 로고    scopus 로고
    • The backward group preserving scheme for 1D backward in time advection-dispersion equation
    • in press
    • Liu, C.-S.; Chang, C.-W.; Chang, J.-R. (2009) : The backward group preserving scheme for 1D backward in time advection-dispersion equation. Num. Methods Partial Diff. Eqns., in press.
    • (2009) Num. Methods Partial Diff. Eqns
    • Liu, C.-S.1    Chang, C.-W.2    Chang, J.-R.3
  • 22
    • 0034746116 scopus 로고    scopus 로고
    • Optimal identification of groundwater pollution sources and parameter identification
    • Mahar, P. S.; Datta, B. (2001) : Optimal identification of groundwater pollution sources and parameter identification. J. Water Resour. Plann. Manage., vol. 127, pp. 20-29.
    • (2001) J. Water Resour. Plann. Manage , vol.127 , pp. 20-29
    • Mahar, P.S.1    Datta, B.2
  • 23
    • 34249835495 scopus 로고
    • Regularization of ill-posed differential problems
    • Mel'nikova, I. V. (1992) : Regularization of ill-posed differential problems. Siberian Math. J., vol. 33, pp. 289-298.
    • (1992) Siberian Math. J , vol.33 , pp. 289-298
    • Mel'nikova, I.V.1
  • 24
    • 0040225041 scopus 로고
    • Stabilized quasireversibility and other nearly best possible meth- ods for non-well posed problems
    • Springer-Verlag, Berlin
    • Miller, K. (1973) : Stabilized quasireversibility and other nearly best possible meth- ods for non-well posed problems. Lecture Notes in Math. Springer-Verlag, Berlin, vol. 316, pp. 161-176.
    • (1973) Lecture Notes in Math , vol.316 , pp. 161-176
    • Miller, K.1
  • 26
    • 0002189557 scopus 로고
    • Pseudo-parabolic partial differential equa- tions
    • Showalter, R. E.; Ting, T. W. (1970) : Pseudo-parabolic partial differential equa- tions. SIAM J. Math. Anal. vol. 1, pp. 1-26.
    • (1970) SIAM J. Math. Anal , vol.1 , pp. 1-26
    • Showalter, R.E.1    Ting, T.W.2
  • 29
    • 0027009117 scopus 로고
    • Simultaneous parameter estimation and contaminant source characterization for coupled groundwater flow and contaminant transport model- ing
    • Wagner, B. J. (1992) : Simultaneous parameter estimation and contaminant source characterization for coupled groundwater flow and contaminant transport model- ing. J. Hydrol. vol. 135, pp. 275-303.
    • (1992) J. Hydrol , vol.135 , pp. 275-303
    • Wagner, B.J.1
  • 30
    • 33144471291 scopus 로고    scopus 로고
    • A Markov random field model of contamination source identification in porous media flow
    • Wang, J.; Zabaras, N. (2006) : A Markov random field model of contamination source identification in porous media flow. Int. J. Heat Mass Transfer, vol. 49, pp. 939-950.
    • (2006) Int. J. Heat Mass Transfer , vol.49 , pp. 939-950
    • Wang, J.1    Zabaras, N.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.