메뉴 건너뛰기




Volumn 27, Issue 3, 2011, Pages

Inverse source problem for a fractional diffusion equation

Author keywords

[No Author keywords available]

Indexed keywords

ANALYTIC CONTINUATION; ANALYTICAL SOLUTIONS; EIGENFUNCTION EXPANSIONS; FRACTIONAL DIFFUSION EQUATION; INVERSE SOURCE PROBLEM; MESH-LESS METHODS; NUMERICAL EXAMPLE; REGULARIZATION SCHEMES; SOURCE TERMS;

EID: 79951779651     PISSN: 02665611     EISSN: 13616420     Source Type: Journal    
DOI: 10.1088/0266-5611/27/3/035010     Document Type: Article
Times cited : (263)

References (37)
  • 1
    • 0027069042 scopus 로고
    • Field study of dispersion in heterogeneous aquifer 2
    • Adams E E and Gelhar L W 1992 Field study of dispersion in heterogeneous aquifer 2 Water Resour. Res. 28 3293-307
    • (1992) Water Resour. Res. , vol.28 , pp. 3293-3307
    • Adams, E.E.1    Gelhar, L.W.2
  • 2
    • 0036650559 scopus 로고    scopus 로고
    • Solution for a fractional diffusion-wave equation defined in a bounded domain
    • Agarwal O P 2002 Solution for a fractional diffusion-wave equation defined in a bounded domain Nonlinear Dyn. 29 145-55
    • (2002) Nonlinear Dyn. , vol.29 , pp. 145-155
    • Agarwal, O.P.1
  • 3
    • 0033986694 scopus 로고    scopus 로고
    • Anomalous transport in laboratory-scale, heterogeneous porous media
    • DOI 10.1029/1999WR900295
    • Berkowitz B, Scher H and Silliman S E 2000 Anomalous transport in laboratory-scale, he (Pubitemid 30042117)
    • (2000) Water Resources Research , vol.36 , Issue.1 , pp. 149-158
    • Berkowitz, B.1    Scher, H.2    Silliman, S.E.3
  • 4
    • 77954142858 scopus 로고    scopus 로고
    • Numerical simulations of 2D fractional subdiffusion problems
    • Brunner H, Ling L and Yamamoto M 2010 Numerical simulations of 2D fractional subdiffusion problems J. Comp. Phys. 229 6613-22
    • (2010) J. Comp. Phys. , vol.229 , pp. 6613-6622
    • Brunner, H.1    Ling, L.2    Yamamoto, M.3
  • 5
    • 70450198851 scopus 로고    scopus 로고
    • Uniqueness in an inverse problem for a onedimensional fractional diffusion equation
    • Cheng J, Nakagawa J, Yamamoto M and Yamazaki T 2009 Uniqueness in an inverse problem for a onedimensional fractional diffusion equation Inverse Problems 25 115002
    • (2009) Inverse Problems , vol.25 , pp. 115002
    • Cheng, J.1    Nakagawa, J.2    Yamamoto, M.3    Yamazaki, T.4
  • 6
    • 36149001420 scopus 로고    scopus 로고
    • A Fourier method for the fractional diffusion equation describing sub-diffusion
    • Chen C, Liu F, Turner I and Anhb V 2007 A Fourier method for the fractional diffusion equation describing sub-diffusion J. Comput. Phys. 227 886-97
    • (2007) J. Comput. Phys. , vol.227 , pp. 886-897
    • Chen, C.1    Liu, F.2    Turner, I.3    Anhb, V.4
  • 8
    • 0001780043 scopus 로고
    • Fractional diffusion equation and relaxation in complex viscoelastic materials
    • Giona M, Gerbelli S and Roman H E 1992 Fractional diffusion equation and relaxation in complex viscoelastic materials Physica A 191 449-53
    • (1992) Physica A , vol.191 , pp. 449-53
    • Giona, M.1    Gerbelli, S.2    Roman, H.E.3
  • 11
    • 13344267706 scopus 로고
    • Regularization tools: A MATLAB package for analysis and solution of discrete ill-Posed problem
    • Hansen P C 1994 Regularization tools: A MATLAB package for analysis and solution of discrete ill-posed problem Numer. Algorithms 6 1-35
    • (1994) Numer. Algorithms , vol.6 , pp. 1-35
    • Hansen, P.C.1
  • 12
    • 0000570697 scopus 로고
    • Analysis of discrete ill-posed problems by means of the L-curve
    • Hansen P C 1992 Analysis of discrete ill-posed problems by means of the L-curve SIAM Rev. 34 561-80
    • (1992) SIAM Rev. , vol.34 , pp. 561-580
    • Hansen, P.C.1
  • 13
    • 0031961373 scopus 로고    scopus 로고
    • Dispersive transport of ions in column experiments: An explanation of long-tailed profiles
    • Hatano Y and Hatano N 1998 Dispersive transport of ions in column experiments: An explanation of long-tailed profiles Water Resour. Res. 34 1027-33 (Pubitemid 28219535)
    • (1998) Water Resources Research , vol.34 , Issue.5 , pp. 1027-1033
    • Hatano, Y.1    Hatano, N.2
  • 15
    • 34547548712 scopus 로고    scopus 로고
    • Finite difference/spectral approximation for the time-fractional diffusion equation
    • Lin Y and Xu C 2007 Finite difference/spectral approximation for the time-fractional diffusion equation J. Comp. Phys. 225 1533-52
    • (2007) J. Comp. Phys. , vol.225 , pp. 1533-1552
    • Lin, Y.1    Xu, C.2
  • 16
    • 77957906609 scopus 로고    scopus 로고
    • A backward problem for the time-fractional diffusion equation
    • Liu J J and Yamamoto M 2010 A backward problem for the time-fractional diffusion equation Appl. Anal. 89 1769-90
    • (2010) Appl. Anal. , vol.89 , pp. 1769-1790
    • Liu J, J.1    Yamamoto, M.2
  • 17
    • 56549085438 scopus 로고    scopus 로고
    • Maximum principle for the generalized time-fractional diffusion equation
    • Luchko Y 2009 Maximum principle for the generalized time-fractional diffusion equation J. Math. Anal. Appl. 351 218-23
    • (2009) J. Math. Anal. Appl. , vol.351 , pp. 218-223
    • Luchko, Y.1
  • 18
    • 76449091249 scopus 로고    scopus 로고
    • Some uniqueness and existence results for the initial-boundary-value problems for the generalized time-fractional diffusion equation
    • Luchko Y 2010 Some uniqueness and existence results for the initial-boundary-value problems for the generalized time-fractional diffusion equation Comput. Math. Appl. 59 1766-72
    • (2010) Comput. Math. Appl. , vol.59 , pp. 1766-1772
    • Luchko, Y.1
  • 19
    • 30244460855 scopus 로고    scopus 로고
    • The fundamental solutions for the fractional diffusion-wave equation
    • Mainadri F 1996 The fundamental solutions for the fractional diffusion-wave equation Appl. Math. Lett. 9 23-8
    • (1996) Appl. Math. Lett. , vol.9 , pp. 23-28
    • Mainadri, F.1
  • 20
    • 70449607356 scopus 로고    scopus 로고
    • Fractional Cauchy problems on bounded domains
    • Meerschaert M M, Nane E and Vellaisamy P 2009 Fractional Cauchy problems on bounded domains Ann. Probab. 37 979-1007
    • (2009) Ann. Probab. , vol.37 , pp. 979-1007
    • Meerschaert M, M.1    Nane, E.2    Vellaisamy, P.3
  • 22
    • 0002641421 scopus 로고    scopus 로고
    • The random walk's guide to anomalous diffusion: A fractional dynamics approach
    • Metzler R and Klafter J 2000 The random walk's guide to anomalous diffusion: A fractional dynamics approach Phys. Rep. 339 1-77
    • (2000) Phys. Rep. , vol.339 , pp. 1-77
    • Metzler, R.1    Klafter, J.2
  • 24
    • 79951781633 scopus 로고    scopus 로고
    • Overview to mathematical analysis for fractional diffusion equations-new mathematical aspects motivated by industrial collaboration
    • Nakagawa J, Sakamoto K and Yamamoto M 2010 Overview to mathematical analysis for fractional diffusion equations-new mathematical aspects motivated by industrial collaboration J. Math. Ind. 2 99-108
    • (2010) J. Math. Ind. , vol.2 , pp. 99-108
    • Nakagawa, J.1    Sakamoto, K.2    Yamamoto, M.3
  • 25
    • 0022492943 scopus 로고
    • REALIZATION OF THE GENERALIZED TRANSFER EQUATION IN A MEDIUM WITH FRACTAL GEOMETRY.
    • Nigmatullin R R 1986 The realization of the generalized transfer equation in a medium with fractal geometry Phys. Stat. Sol. B 133 425-30 (Pubitemid 16505297)
    • (1986) Physica Status Solidi (B) Basic Research , vol.133 , Issue.1 , pp. 425-430
    • Nigmatullin, R.R.1
  • 26
    • 50049102930 scopus 로고    scopus 로고
    • Fractional diffusion-wave problem in cylindrical coordinates
    • Ozdemir N and Karadeniz D 2008 Fractional diffusion-wave problem in cylindrical coordinates Phys. Lett. A 372 5968-72
    • (2008) Phys. Lett. A , vol.372 , pp. 5968-5972
    • Ozdemir, N.1    Karadeniz, D.2
  • 28
    • 78049345257 scopus 로고    scopus 로고
    • Mittag-Leffler function
    • Podlubny I Mittag-Leffler function TheMATLAB routine http://www. mathworks.com/matlabcentral/fileexchange
    • The MATLAB Routine
    • Podlubny, I.1
  • 29
    • 21344498117 scopus 로고
    • Continuous-time random walks and the fractional diffusion equation
    • Roman H E and Alemany P A 1994 Continuous-time random walks and the fractional diffusion equation J. Phys. A: Math. Gen. 27 3407-10
    • (1994) J. Phys. A: Math. Gen. , vol.27 , pp. 3407-3410
    • Roman, H.E.1    Alemany, P.A.2
  • 32
    • 30744474991 scopus 로고    scopus 로고
    • A full discrete difference scheme for a diffusion-wave system
    • Sun Z Z and Wu X N 2006 A full discrete difference scheme for a diffusion-wave system Appl. Numer. Math. 56 193-209
    • (2006) Appl. Numer. Math. , vol.56 , pp. 193-209
    • Sun, Z.Z.1    Wu X, N.2
  • 33
    • 33947374025 scopus 로고    scopus 로고
    • A generalization of Duhamel's principle for differential equations of fractional order
    • DOI 10.1134/S1064562407010267
    • Umarov S R and Saidamatov E M 2007 A Generalization of Duhamels principle for differential equations of fractional order Dokl. Math. 75 94-6 (Pubitemid 46446523)
    • (2007) Doklady Mathematics , vol.75 , Issue.1 , pp. 94-96
    • Umarov, S.R.1    Saidamatov, E.M.2
  • 34
    • 0002328596 scopus 로고
    • A survey of some smoothing problems and themethod of generalized cross-validation for solving them
    • (Amsterdam: North-Holland)
    • Wahba G 1977 A survey of some smoothing problems and themethod of generalized cross-validation for solving them Applications of Statistics (Amsterdam: North-Holland) pp 507-23
    • (1977) Applications of Statistics , pp. 507-523
    • Wahba, G.1
  • 35
    • 79951797121 scopus 로고    scopus 로고
    • Carleman estimate for a fractional diffusion equation with half-order and application
    • accepted
    • Xu X, Cheng J and Yamamoto M 2011 Carleman estimate for a fractional diffusion equation with half-order and application Appl. Anal. accepted
    • (2011) Appl. Anal.
    • Xu, X.1    Cheng, J.2    Yamamoto, M.3
  • 36
    • 33745970843 scopus 로고    scopus 로고
    • Modeling solute transport in one-dimensional homogeneous and heterogeneous soil columns with continuous time random walk
    • DOI 10.1016/j.jconhyd.2006.03.001, PII S0169772206000568
    • Xiong Y, Huang G and Huang Q 2006 Modeling solute transport in one-dimensional homogeneous and heterogeneous soil columns with continuous-time random walk J. Contaminant Hydrol. 86 163-75 (Pubitemid 44067278)
    • (2006) Journal of Contaminant Hydrology , vol.86 , Issue.3-4 , pp. 163-175
    • Xiong, Y.1    Huang, G.2    Huang, Q.3
  • 37
    • 0043131921 scopus 로고    scopus 로고
    • Application of the fractional advection-dispersion equation in porous media
    • Zhou L and Selim H M 2003 Application of the fractional advection-dispersion equations in porous media Soil Sci. Soc. Am. J. 67 1079-84 (Pubitemid 36940977)
    • (2003) Soil Science Society of America Journal , vol.67 , Issue.4 , pp. 1079-1084
    • Zhou, L.1    Selim, H.M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.