[1]
|
Yamamoto, M. (1993) Conditional Stability in Determination of Force Terms of Heat Equations in a Rectangle. Mathematical and Computer Modelling, 18, 79-88.
|
[2]
|
Isakov, V. (1999) Some Inverse Problems for the Diffusion Equation. Inverse Problems, 15, 3-10.
https://doi.org/10.1088/0266-5611/15/1/004
|
[3]
|
Isakov, V. (1991) Inverse Parabolic Problems with the Final Overdetermination. Communications on Pure and Applied Mathematics, 54, 185-209.
|
[4]
|
Bushuyev, I. (1995) Global Uniqueness for Inverse Parabolic Problems with Final Observation. Inverse Problems, 11, L11-L16. https://doi.org/10.1088/0266-5611/11/4/001
|
[5]
|
Li, G.S. and Yamamoto, M. (2006) Stability Analysis for Determining a Source Term in a 1-D Advection-Dispersion Equation. Journal of Inverse and Ill-Posed Problems, 14, 147-155. https://doi.org/10.1515/156939406777571067
|
[6]
|
李功胜, 贾现正, 孙春龙, 杜殿虎. 对流弥散方程线性源项系数反演的变分伴随方法[J]. 应用数学学报, 2015, 38(6): 1001-1015.
|
[7]
|
Isakov, V. (1998) Inverse Problems for Partial Differential Equations. Spring-Verlag, New York.
https://doi.org/10.1007/978-1-4899-0030-2
|
[8]
|
Du Chateau, P. and Rundell, W. (1985) Unicity in an Inverse Problem for an Unknown Term in a Reaction Diffusion Equation. J. Differential Equations, 59, 155-164. https://doi.org/10.1016/0022-0396(85)90152-4
|
[9]
|
Du Chateau, P. (1995) Monotomicity and Invertibility of Coefficient to Data Mapping for Parabolic Inverse Problems. SIAM Journal on Mathematical Analysis, 26, 1473-1487. https://doi.org/10.1137/S0036141093259257
|
[10]
|
Du Chateau, P. (1997) An Inverse Problem for the Hydraulic Properties of Porous Media. SIAM Journal on Mathematical Analysis, 28, 611-632. https://doi.org/10.1137/S0036141095285673
|
[11]
|
Du Chateau, P., Thelwell, R. and Butters, M. (2004) Analysis of an Adjoint Problem Approach to the Identification of an Unknown Diffusion Coefficient. Inverse problems, 20, 601-625. https://doi.org/10.1088/0266-5611/20/2/019
|
[12]
|
Hasanov, A., Du Chateau, P. and Petkas, B. (2006) An Adjoint Problem Approach and Coarsefine Mesh Method for Identification of the Diffusion in a Linear Parabolic Equation. Journal of Inverse and Ill-Posed Problems, 14, 435-463.
https://doi.org/10.1515/156939406778247615
|
[13]
|
Du Chateau, P. (2013) An Adjoint Method for Proving Identifiability of Coefficients in Parabolic Equations. Journal of Inverse and Ill-Posed Problems, 21, 639-663.
|
[14]
|
刘倩, 李功胜, 王桢东. 一个二维对流扩散方程源项反问题的条件唯一性[J]. 应用数学进展, 2016, 5(4): 591-597.
|
[15]
|
Choulli, M. and Yamamoto, M. (2004) Conditional Stability in Determining a Heat Source. Journal of Inverse and Ill-Posed Problems, 12, 233-244. https://doi.org/10.1515/1569394042215856
|
[16]
|
McCamy, R.C., Mizel, V.J. and Seidman, T.I. (1968) Approximate Boundary Controllability of the Heat Equation. Journal of Mathematical Analysis and Applications, 23, 699-703. https://doi.org/10.1016/0022-247X(68)90148-0
|
[17]
|
李功胜, 姚德. 扩散模型的源项反演及其应用[M]. 北京: 科学出版社, 2014.
|
[18]
|
娄和忠. 溶质运移模型与多参数反演算法[D]: [硕士学位论文]. 淄博: 山东理工大学, 2012.
|
[19]
|
孙春龙, 含多个时间分数阶反常扩散方程的反问题研究[D]: [硕士学位论文]. 淄博: 山东理工大学, 2016.
|
[20]
|
Li, G.S., Cheng, J., Yao, D., Liu, H.L. and Liu, J.J. (2007) One-Dimensional Equilibrium Model and Source Parameter Determination for Soil-Column Experiment. Applied Mathematics and Computation, 190, 1365-1374.
https://doi.org/10.1016/j.amc.2007.02.064
|
[21]
|
Li, G.S., Tan, Y.J., Yao, D., Wang, X.Q. and Liu, H.L. (2008) A Nonlinear Mathematical Model for an Undisturbed Soil-Column Experiment and Source Parameter Identification. Inverse Problems in Science and Engineering, 16, 885-901. https://doi.org/10.1080/17415970802015880
|