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Volumn 89, Issue 11, 2010, Pages 1769-1788

A backward problem for the time-fractional diffusion equation

Author keywords

Diffusion process; Fractional derivative; Inverse problem; Numerics; Regularization

Indexed keywords


EID: 77957906609     PISSN: 00036811     EISSN: 1563504X     Source Type: Journal    
DOI: 10.1080/00036810903479731     Document Type: Article
Times cited : (245)

References (23)
  • 4
    • 0004011174 scopus 로고
    • Inproperly Posed Problems in Partial Differential Equations
    • Regional Series Conferences in Applied Mathematics, Philadelphia
    • L.E. Payne, Inproperly Posed Problems in Partial Differential Equations, SIAM, Regional Series Conferences in Applied Mathematics, Philadelphia, 1975.
    • (1975) SIAM
    • Payne, L.E.1
  • 5
    • 30544431837 scopus 로고    scopus 로고
    • Regularization and error estimates for nonhomogeneous backward heat problems
    • T.D. Duc and N.H. Tuan, Regularization and error estimates for nonhomogeneous backward heat problems, Electron. J. Diff. Eqns. 2006(4) (2006), pp. 1-10.
    • (2006) Electron. J. Diff. Eqns , vol.2006 , Issue.4 , pp. 1-10
    • Duc, T.D.1    Tuan, N.H.2
  • 6
    • 0040757108 scopus 로고
    • A mollified space-marching finite-difference algorithm for the two-dimensional inverse heat conduction problem with slab symmetry
    • L. Guo and D.A. Murio, A mollified space-marching finite-difference algorithm for the two-dimensional inverse heat conduction problem with slab symmetry, Inverse Probl. 7(2) (1991), pp. 247-259.
    • (1991) Inverse Probl , vol.7 , Issue.2 , pp. 247-259
    • Guo, L.1    Murio, D.A.2
  • 7
    • 0001605874 scopus 로고    scopus 로고
    • Approximate inverse for a one-dimensional inverse heat conduction problem
    • P. Jonas and A.K. Louis, Approximate inverse for a one-dimensional inverse heat conduction problem, Inverse Probl. 16(1) (2000), pp. 175-185.
    • (2000) Inverse Probl , vol.16 , Issue.1 , pp. 175-185
    • Jonas, P.1    Louis, A.K.2
  • 8
    • 0005001094 scopus 로고    scopus 로고
    • The decomposition approach to inverse heat conduction
    • D. Lesnic and L. Elliott, The decomposition approach to inverse heat conduction, J. Math. Anal. Appl. 232(1) (1999), pp. 82-98.
    • (1999) J. Math. Anal. Appl , vol.232 , Issue.1 , pp. 82-98
    • Lesnic, D.1    Elliott, L.2
  • 9
    • 0012905852 scopus 로고    scopus 로고
    • Determination of temperature field for backward heat transfer
    • J.J. Liu, Determination of temperature field for backward heat transfer, Comm. Korean Math. Soc. 16(3) (2001), pp. 385-397.
    • (2001) Comm. Korean Math. Soc , vol.16 , Issue.3 , pp. 385-397
    • Liu, J.J.1
  • 10
    • 0037102596 scopus 로고    scopus 로고
    • Numerical solution of forward and backward problem for 2-D heat conduction problem
    • J.J. Liu, Numerical solution of forward and backward problem for 2-D heat conduction problem, J. Comput. Appl. Maths. 145(2) (2002), pp. 459-482.
    • (2002) J. Comput. Appl. Maths , vol.145 , Issue.2 , pp. 459-482
    • Liu, J.J.1
  • 11
    • 77957900527 scopus 로고    scopus 로고
    • International Conference on Inverse Problems - Recent Development in Theories and Numerics, Y.C. Hon, M. Yamamoto, J. Cheng, and J.Y. Lee, World Scientific, Singapore
    • J.J. Liu, On stability estimate for a backward heat transfer problem, in International Conference on Inverse Problems - Recent Development in Theories and Numerics, Y.C. Hon, M. Yamamoto, J. Cheng, and J.Y. Lee, eds., World Scientific, Singapore, 2003, pp. 134-142.
    • (2003) On Stability Estimate For a Backward Heat Transfer Problem , pp. 134-142
    • Liu, J.J.1
  • 12
    • 0037256898 scopus 로고    scopus 로고
    • On stability and regularization for backward heat equation
    • J.J. Liu and D.J. Lou, On stability and regularization for backward heat equation, Chin. Ann. Math. Ser. B 24(1) (2003), pp. 35-44.
    • (2003) Chin. Ann. Math. Ser. B , vol.24 , Issue.1 , pp. 35-44
    • Liu, J.J.1    Lou, D.J.2
  • 14
    • 62649111488 scopus 로고    scopus 로고
    • A two-dimensional inverse heat conduction problem for estimating heat flux
    • A. Shidfar and A. Neisy, A two-dimensional inverse heat conduction problem for estimating heat flux, Far East J. Appl. Math. 10(2) (2003), pp. 145-150.
    • (2003) Far East J. Appl. Math , vol.10 , Issue.2 , pp. 145-150
    • Shidfar, A.1    Neisy, A.2
  • 15
    • 0039633096 scopus 로고
    • The final value problem for evolution equations
    • R.E. Showalter, The final value problem for evolution equations, J. Math. Anal. Appl. 47 (1974), pp. 563-572.
    • (1974) J. Math. Anal. Appl , vol.47 , pp. 563-572
    • Showalter, R.E.1
  • 16
    • 0033884660 scopus 로고    scopus 로고
    • Boundary value problems for fractional diffusion equations
    • R. Metzler and J. Klafter, Boundary value problems for fractional diffusion equations, Physica A 278 (2000), pp. 107-125.
    • (2000) Physica A , vol.278 , pp. 107-125
    • Metzler, R.1    Klafter, J.2
  • 18
    • 34547548712 scopus 로고    scopus 로고
    • Finite difference/spectral approximation for the time-fractional diffusion equation
    • Y. Lin and C. Xu, Finite difference/spectral approximation for the time-fractional diffusion equation, J. Comput. Phys. 225 (2007), pp. 1533-1552.
    • (2007) J. Comput. Phys , vol.225 , pp. 1533-1552
    • Lin, Y.1    Xu, C.2
  • 19
    • 25444472344 scopus 로고    scopus 로고
    • An explicit finite difference method and a new Von Neumann-type stability analysis for fractional diffusion equations
    • S.B. Yuste and L. Acedo, An explicit finite difference method and a new Von Neumann-type stability analysis for fractional diffusion equations, SIAM J. Num. Anal. 42(5) (2005), pp. 1862-1874.
    • (2005) SIAM J. Num. Anal , vol.42 , Issue.5 , pp. 1862-1874
    • Yuste, S.B.1    Acedo, L.2
  • 21
    • 77957900310 scopus 로고    scopus 로고
    • Inverse source problems for diffusion equations and fractional diffusion equations
    • Graduate School of Mathematical Sciences, The University of Tokyo
    • K. Sakamoto, Inverse source problems for diffusion equations and fractional diffusion equations, Doctoral dissertation, Graduate School of Mathematical Sciences, The University of Tokyo, 2009.
    • (2009) Doctoral Dissertation
    • Sakamoto, K.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.