|
[2]WEN J, YAMAMOTO M, WEI T. Simultaneous determination of a time-dependent heat source and the initial temperature in an inverse heat conduction problem[J]. Inverse Problems in Science and Engineering,2013,21(3): 485-499.
|
|
ISAKOV V. Inverse Problems for Partial Differential Equations[M]. New York: Springer-Verlag, 1998.
|
|
[3]JOURHMANE M, MERA N S. An iterative algorithm for the backward heat conduction problem based on variable relaxation factors[J]. Inverse Problems in Engineering,2002,10(4): 293-308.
|
|
[4] LIU J J, WANG B X. Solving the backward heat conduction problem by homotopy analysis method[J]. Applied Numerical Mathematics,2018,128: 84-97.
|
|
[5]XIONG X T, FU C L, QIAN Z. Two numerical methods for solving a backward heat conduction problem[J]. Applied Mathematics and Computation,2006,179(1): 370-377.
|
|
[6] WANG Z W, QIU S F, RUAN Z S, et al. A regularized optimization method for identifying the space-dependent source and the initial value simultaneously in a parabolic equation[J]. Computers & Mathematics With Applications,2014,67(7): 1345-1357.
|
|
[7]FU C L, XIONG X T, QIAN Z. Fourier regularization for a backward heat equation[J]. Journal of Mathematical Analysis & Applications,2007,331(1): 472-480.
|
|
[8] CHENG W, FU C L. A modified Tikhonov regularization method for an axisymmmetric backward heat equation[J]. Acta Mathematica Sinica,2010,26(11): 2157-2164.
|
|
[9]CHENG W, MA Y J, FU C L. A regularization method for solving the radially symmetric backward heat conduction problem[J]. Applied Mathematics Letters,2014,30: 38-43.
|
|
[10]THOMAS M D A, BAMFORTH P B. Modelling chloride diffusion in concrete: effect of fly ash and slag[J]. Cement & Concrete Research,1999,29(4): 487-495.
|
|
[11]TUAN N H, QUAN P H, TRONG D D, et al. On a backward heat problem with time-dependent coefficient: regularization and error estimates[J]. Applied Mathematics and Computation,2013,219(11): 6066-6073.
|
|
[12]TUAN N H, HOA N V. Determination temperature of a backward heat equation with time-dependent coefficients[J]. Mathematica Slovaca,2012, 62(5): 937-948.
|
|
[13]TRIET L M, QUAN P H, TRONG D D, et al. A backward parabolic equation with a time-dependent coefficient: regularization and error estimates[J]. Journal of Computational and Applied Mathematics,2013,237(1): 432-441.
|
|
[14]QUAN P H, TRIET L M, TRONG D D, et al. A regularization of the backward problem for nonlinear parabolic equation with time-dependent coefficient[J]. International Journal of Mathematics and Mathematical Sciences,2012,109: 1-20.
|
|
[15]ZHANG H W, ZHANG X J. Iterative method based on the truncated technique for backward heat conduction problem with variable coefficient[J]. Open Access Library Journal,2015,2(4): 1-11.
|
|
[16]WANG J G, WEI T. An iterative method for backward time-fractional diffusion problem[J]. Numerical Methods for Partial Differential Equations,2014,30(6): 2029-2041.
|
|
[17]DENG Y J, LIU Z H. Iteration methods on sideways parabolic equations[J]. Inverse Problem,2009,25(9): 095004.
|
|
[18]WANG Z X, GUO D R. Introduction to Special Function[M]. Beijing: Peking University Press, 2000.
|
|
[19]ABRAMOWITZ M. Handbook of Mathematical Functions: With Formulas, Graphs and Mathematical Tables[M]. New York: Dover Publications Inc, 1965.
|
|
[20]柳重堪. 正交函数及其应用[M]. 北京: 国防工业出版社, 1982.(LIU Zhongkan. Orthogonal Function and its Application[M]. Beijing: National Defense Industry Press, 1982.(in Chinese))
|
|
[21]NEGGAL B, BOUSSETIAL N, REBBANI F. Projected Tikhonov regularization method for Fredholm integral equations of the first kind[J]. Journal of Inequalities and Applications,2016,2016: 195. DOI: 10.1186/s13660-016-1137-6.
|
|
[22]TAUTENHAHN U. Optimality for ill-posed problems under general source conditions[J]. Numerical Functional Analysis and Optimization,1998,19: 377-398.
|
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