References
- Lavrent'ev, M, Romanov, V, and Shishatskij, S, 1986. Ill-posed Problems of Mathematical Physics and Analysis, Translations of Mathematical Monographs. Vol. 64. Providence, RI: Transl. from the Russian by JR Schulenberger, American Mathematical Society; 1986.
- Isakov, V, 2006. Inverse Problems for Partial Differential Equations. New York: Springer Verlag; 2006.
- Showalter, R, 1974. The final value problem for evolution equations, J. Math. Anal. Appl 47 (1974), pp. 563–572.
- Ames, K, Clark, G, Epperson, J, and Oppenheimer, S, 1998. A comparison of regularizations for an ill-posed problem, Math. Comput. 67 (1998), pp. 1451–1471.
- Seidman, T, 1996. Optimal filtering for the backward heat equation, SIAM J. Numer. Anal. 33 (1996), pp. 162–170.
- Mera, N, Elliott, L, Ingham, D, and Lesnic, D, 2001. An iterative boundary element method for solving the one-dimensional backward heat conduction problem, Int. J. Heat Mass Transfer 44 (2001), pp. 1937–1946.
- Hào, D, 1994. A mollification method for ill-posed problems, Numer. Math. 68 (1994), pp. 469–506.
- Liu, C, 2004. Group preserving scheme for backward heat conduction problems, Int. J. Heat Mass Transfer 47 (2004), pp. 2567–2576.
- Kirkup, S, and Wadsworth, M, 2002. Solution of inverse diffusion problems by operator-splitting methods, Appl. Math. Model. 26 (2002), pp. 1003–1018.
- Fu, C, Xiong, X, and Qian, Z, 2007. Fourier regularization for a backward heat equation, J. Math. Anal. Appl. 331 (2007), pp. 472–480.
- Dou, F, Fu, C, and Yang, F, 2009. Optimal error bound and Fourier regularization for identifying an unknown source in the heat equation, J. Comput. Appl. Math. 230 (2009), pp. 728–737.
- Engl, HW, Hanke, M, and Neubauer, A, 1996. Regularization of Inverse Problems. The Netherlands: Springer; 1996.