参考文献/References:
[1] Isakov V.Inverse problems for partial differental equation[M].New York:Springer-Verlag,1998.
[2] Lattés R,Lions J L.The method of quasi-reversibility:applications to partial differental equations[M].New York:American Elseiver,1969.
[3] Miller K.Stablized quasi-reversibility and other nearly-best-possible methods for non-well-possed problems[M]∥Knops R J.Symposium on non-well-posed problems and logarthmic convexity.Berlin:Springer-Verlag,1973:161-176.
[4] Wang Jungang,Wei Ting.Quasi-reversibility method to identify a space-dependent source for the time-fractional diffusion equation[J].Applied Mathematical Modelling,2015,39(20):6139-6149.
[5] Li Xiaoxiao,Yang Fan,Liu Jie,et al.The quasi-reversibility regularization method for identifying the unknown source for the modified Helmholtz equation[J].Journal of Applied Mathematics,2013,2013(2):245963.
[6] Liu Jichuan,Wei Ting.A quasi-reversibility regularization method for an inverse heat conduction problem without intial data[J].Applied Mathematics and Computation,2013,219(23):10866-10881.
[7] Yang Fan,Fu Chuli.The quasi-reversibility regularization method for identifying the unknown source for time fractional diffusion equation[J].Applied Mathematical Modelling,2015,39(5/6):1500-1512.[8] Zhao Zhenyu,Meng Zehong.A modified Tikhonov regularization method for a backward heat equation[J].Inver Problems in Science and Engineering,2011,19(8):1175-1182.
[9] Su Lingde,Jiang Tongsong.Numerical method for solving nonhomogeneous backward heat conduction problem[J].International Journal of Differential Equations,2018,2018:1868921.
[10] Ku Chengyu,Liu Chihyu,Yeih Weichung,et al.A novel space-time meshless method for solving the backward heat conduction problem[J].International Journal of Heat and Mass Transfer,2019,130:109-122.
[11] Fu Chuli,Xiong Xiangtuan,Qian Zhi.Fourier regularization for a backward heat equation[J].Journal of Mathematical Analysis and Application,2007,331(1):472-480.
[12] Eldén L.Approximations for a Cauchy problem for the heat equation[J].Inverse Problems,1987,3(2):263-273.
[13] Weber C F.Analysis and solution of the ill-posed inverse heat conduction problem[J].International Journal of Heat and Mass Transfer,1981,24(11):1783-1792.
[14] Qian Zhi,Fu Chuli,Feng Xiaoli.A modified method for high order numerical derivatives[J].Applied Mathematics and Computation,2006,182(2):1191-1200.
[15] Qian Zhi,Fu Chuli,Xiong Xiangtuan.A modified method for a non-standard inverse heat conduction problem[J].Applied Mathematics and Computation,2006,180(2):453-468.
[16] Liu Jijun,Yamamoto M.A backward problem for the time-fractional diffusion equation[J].Applicable Analysis,2010,89(11):1769-1788.
[17] Qian Ailin,Xiong Xiangtuan,Wu Yujiang.On a quasi-reversibility regularization method for a Cauchy problem of the Helmholtz equation[J].Journal of Computation and Applied Mathematics,2010,233(8):1969-1979.
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