Uniqueness for inverse problems of determining orders of multi-term time-fractional derivatives of diffusion equation

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Li, Zhiyuan; Yamamoto, Masahiro;

This article proves the uniqueness for two kinds of inverse problems of identifying fractional orders in diffusion equations with multiple time-fractional derivatives by pointwise observation. By means of eigenfunction expansion and Laplace transform, we reduce the uniq... View more
  • References (17)
    17 references, page 1 of 2

    [1] E. E. Adams and L. W. Gelhar, Field study of dispersion in a heterogeneous aquifer 2: spatial moments analysis Water Resources Res. 28(1992), 32933307.

    [2] S. Beckers, M. Yamamoto, Regularity and unique existence of solution to linear diffusion equation with multiple time-fractional derivatives, in: K. Bredies, C. Clason, K. Kunisch, G. von Winckel (Eds.), Control and Optimization with PDE Constraints, Birkh¨auser, Basel, 2013, pp. 45-56.

    [3] M. Cheng, J. Nakagawa, M. Yamamoto and T. Yamazaki, Uniqueness in an inverse problem for a one dimensional fractional diffusion equation. Inverse Problems 25 (2009) 115002.

    [4] R. Courant, D. Hilbert, Methods of Mathematical Physics, Wiley-VCH, 1989.

    [5] K. Diethelm and Y. Luchko, Numerical solution of linear multi-term initial value problems of fractional order. J. Comput. Anal. Appl. 6 (2004), 243-263.

    [6] Y. Hatno, N. Hatano, Dispersive transport of ions in column experiments: an explanation of long-tailed profiles, Water Resources Res. 34(1980) 1027-1033.

    [7] Y. Hatano, Junichi Nakagawa, Shengzhang Wang, M. Yamamoto, Determination of order in fractional diffusion equation. J. Math-for-Ind. 5A (2013), 5157.

    [8] Gongsheng Li, Dali Zhang, Xianzheng Jia, M. Yamamoto, Simultaneous inversion for the space-dependent diffusion coefficient and the fractional order in the time-fractional diffusion equation. Inverse Problems 29 (2013), no. 6, 065014, 36 pp.

    [9] Zhiyuan Li, M. Yamamoto, Initial-boundary value problems for linear diffusion equation with multiple time-fractional derivatives, arXiv:1306.2778v2, 2013.

    [10] Zhiyuan Li, Yikan Liu and M. Yamamoto, Initial-boundary value problems for multi-term time-fractional diffusion equations with positive constant coefficients, arXiv: 1312.2112, 2013.

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