科研项目：
11. 国家自然科学基金面上项目，11971104，基于抛物型方程反问题的扩散过程的参数反演及应用，2020/01-2023/12，在研，主持。
10. 国家自然科学基金重点项目，11531005，基于医学影像的病灶识别的数学方法及理论，2016/01-2020/12，在研，参加。
09. 国家自然科学基金重大研究计划(集成)项目，91730304，数据同化的数学理论与方法，2018/01-2019/12，结题，参加。
08. 国家自然科学基金中日韩A3前瞻计划项目，11421110002，应用反问题的建模与计算，2014/08-2019/07，结题，参加。
07. 国家自然科学基金重大研究计划(培育)项目，91330109，基于微分方程模型的介质成像和图像处理的数值方法，2014/01-2016/12，结题，主持。
06. 国家自然科学基金中德芬国际合作项目，11161130002，带有阻尼边界的逆散射问题，2011/01-2013/12，结题，主持。
05. 国家自然科学基金面上项目，11071039，椭圆型方程边界反演及在逆散射中的应用，2011/01-2013/12，结题，主持。
04. 国家自然科学基金天元专项，10926178，磁共振成像的降噪技术和数值方法，2010/01-2010/12，结题，主持。
03. 国家自然科学基金国际合作项目，10911140265，核磁共振成像的算法实现，2009/06-2011/05，结题，主持。
02. 国家自然科学基金面上项目，10771033，椭圆型方程反问题及数值解，2008/01-2010/12，结题，主持。
01. 国家自然科学基金面上项目，10371018，高维微分方程反问题的正则化方法及数值解，2004/01-2006/12，结题，主持。
学术论文：
98. J.J.Liu, L.Y.Wang, Q.Zhang, S.T.Yau, The dynamical model for COVID-19 with asymptotic analysis and numerical implementations, Appl. Math. Modeling, DOI: https://doi.org/10.1016/j.apm.2020.07.057.
97. J.J.Liu, M.Machida, G.Nakamura, G.Nishimura, C.L.Sun, On fluorescence imaging: diffusion equation model and recovery of absorption coefficient of fluorophores, Science China Mathematics, DOI: https://doi.org/10.1007/s11425-020-1731-y.
96. M.M.Zhang, J.J.Liu, Recovery of non-smooth radiative coefficient from nonlocal observation by diffusion system, J. Inverse and Ill-posed Problems, 28(3), 389-410, 2020.
95. C.L.Sun, J.J.Liu, An inverse source problem for distributed order time-fractional diffusion equation, Inverse Problems, 33(5), 055008, 2020.
94. X.M.Liu, J.J.Liu, Image restoration from noisy incomplete frequency data by alternative iteration scheme, Inverse Problems and Imaging, 14(4), 583–606, 2020.
93. J.Cheng, J.J.Liu, An inverse source problem for parabolic equations with local measurements, Appl. Math. Lett., 103, 106213, 2020.
92. C.L.Sun, G.Nakamura, G.Nishimura, Y.Jiang, J.J.Liu, M.Machida, Fast and robust reconstruction algorithm for fluorescence diffuse optical tomography assuming a cuboid target, J. Opt. Soc. Amer., Ser.A, 37(2), 231-239, 2020.
91. C.L.Sun, J.J.Liu, Reconstruction of the space-dependent source from partial Neumann data for slow diffusion system, Acta Mathematicae Applicatae Sinica, English Ser., 36(1), 166-182, 2020.
90. L.Y.Wang, J.J.Liu, On fluorophore imaging by diffusion equation model: decompositions and optimizations, Acta Mathematicae Applicatae Sinica, English Ser., 36(1), 203-222, 2020.
89. D.N.Hao, J.J.Liu, N.V.Duc and N.V.Thang, Stability results for backward time-fractional parabolic equations, Inverse Problems, 35(12), 125006, 2019.
88. M.M.Zhang, J.J.Liu, Identification of a time-dependent source term in a distributed-order time-fractional equation from a nonlocal integral observation, Computers and Mathematics with Applications, 78(10), 3375-3389, 2019.
87. J.Cheng, J.J.Liu, B.Zhang, Inverse problems for PDEs: models, computations and applications (in Chinese), Scientia Sinica Mathematica, 49, 643-666, 2019.
86. X.M.Liu, J.J.Liu, On image restoration from random sampling noisy frequency data with regularization, Inverse Problems in Sciences and Engineering, 27(12), 1765-1789, 2019.
85. Y.C.Wang, J.J.Liu, On the edge detection of an image by numerical differentiations for gray function, Mathematical Methods in the Applied Sciences, 41(6), 2466-2479, 2018.
84. J.J.Liu, B.X.Wang, Solving the backward heat transfer problem by homotopy analysis method, Appl. Numer. Math., 128, 84-97, 2018.
83. Y.C.Wang, J.J.Liu, Identification of non-smooth boundary heat dissipation by partial boundary data, Appl. Math. Lett., 69, 42-48, 2017.
82. Y.C.Wang, J.J.Liu, On the simultaneous recovery of boundary heat transfer coefficient and initial heat status, J. Inverse and Ill-posed Problems, 25(5), 597-616, 2017.
81. M.Zhong, J.J.Liu, On the reconstruction of media inhomogeneity by inverse wave scattering model, Science China Mathematics, 60(10), 1825-1836, 2017.
80. J.J.Liu, G.Nakamura, Recovering the boundary corrosion from electrical potential distribution using partial boundary data, Inverse Problems and Imaging, 11(3), 521-538, 2017.
79. H.B.Wang, J.J.Liu, An inverse scattering problem with generalized oblique derivative boundary condition, Appl. Numer. Math., 108, 226-241, 2016.
78. T.X.Li, J.J.Liu, Transmission eigenvalue problem for inhomogeneous absorbing media with mixed boundary condition, Science China Mathematics, 59(6), 1081-1094, 2016.
77. J.J.Liu, Y.C.Wang, On the reconstruction of boundary impedance of a heat conduction system from nonlocal measurement, Inverse Problems, 32(7), 075002, 2016.
76. B.X.Wang, J.J.Liu, Recovery of thermal conductivity in two-dimensional media with nonlinear source by optimizations, Appl. Math. Lett., 60, 73-80, 2016.
75. L.Y.Wang, B.Zhou, J.J.Liu, Simultaneous recovery of the temperature and species concentration from integral equation model, Appl. Math. Model., 40(4), 3090-3103, 2016.
74. J.J.Liu, M.Yamamoto, L.L.Yan, On the reconstruction of unknown time-dependent boundary sources for time fractional diffusion process by distributing measurement, Inverse Problems, 32(1), 015009, 2016.
73. H.B.Wang, J.J.Liu, The two-dimensional direct and inverse scattering problems with generalized oblique derivative boundary condition, SIAM J. Appl. Math., 75(2), 313-334, 2015.
72. T.X.Li, W.Q.Huang, W.W.Lin, J.J.Liu, On spectral analysis anda novel algorithm for transmission eigenvalue problems, J. Sci. Comput., 64, 83-108, 2015.
71. J.J.Liu, M.Yamamoto, L.Yan, On the uniqueness and reconstruction for an inverse problem of the fractional diffusion process, Appl. Num. Math., 87(1), 1-19, 2015.
70. M.Yang, J.J.Liu, Fourier regularization for a final value time-fractional diffusion problem, Applicable Analysis, 94(7), 1508-1526, 2015.
69. Y.Q.Hu, F.Cakoni, J.J.Liu, The inverse scattering problem for a partially coated cavity with interior measurements, Applicable Analysis, 93(5), 936-956, 2014.
68. Q.Chen, J.J.Liu, On the error estimate of the harmonic B_z algorithm in MREIT from noisy magnetic flux field, Chinese Anns. Math. (Ser.B), 35(3), 319-336, 2014.
67. L.Y.Wang, J.J.Liu, Total variation regularization for backward time-fractional diffusion problem, Inverse Problems, 29(11), 115013, 2013.
66. J.J.Liu, H.F.Zhao, On the reconstruction of obstacle using MFS from the far field data, Inverse Problems in Science and Engineering, 21(4), 682-703, 2013.
65. H.L.Xu, J.J.Liu, On the Laplacian operation by Lavrentiev regularization with applications in medical imaging, Inverse Problems in Science and Engineering, 21(2), 251-268, 2013.
64. M.Yang, J.J.Liu, Solving a final value fractional evolution problem by boundary condition regularization, Appl. Numer. Math., 66, 45-58, 2013.
63. H.B.Wang, J.J.Liu, On decomposition method for acoustic wave scattering by multiple obstacles, Acta Mathematica Scientia, 33B(1), 1-22, 2013.
62. H.F.Zhao, L.Yan, J.J.Liu, On the interface identification of free boundary problem by method of fundamental solution, Numerical Linear Algebra with Applications, 20(2), 385-396, 2013.
61. H.B.Wang, J.J.Liu, A decomposition scheme for acoustic obstacle scattering in a multilayered medium, Applicable Analysis, 92(4), 831-854, 2013.
60. B.Wu, J.J.Liu, Determination of an unknown source for a thermoelastic system with memory effect, Inverse Problems, 28(9), 095012, 2012.
59. Z.W.Wang, J.J.Liu, Identification of the pollution source from 1-dimensional parabolic equation models, Applied Mathematics and Computation, 219(8), 3403-3413, 2012.
58. L.Y.Wang, J.J.Liu, Data regularization for a backward time-fractional diffusion problem, Computers and Mathematics with Applications, 64(11), 3613-3626, 2012.
57. Q.Chen, J.J.Liu, Solving the backward heat conduction problem by data fitting with multiple regularizing parameters, J. Comput. Math., 30(4), 418-432, 2012.
56. Dietmar Homberg, Jijun Liu, Nataliya Togobytska, Identification of the thermal growth characteristics of coagulated tumor tissue in laser-induced thermotherapy, Mathematical Methods in the Applied Sciences, 35(5), 497-509, 2012.
55. H.B.Wang, J.J.Liu, On the reconstruction of surface impedance from the far-field data in inverse scattering problems, Applicable Analysis, 91(4), 787-806, 2012.
54. H.B.Wang, J.J.Liu, Recovering the Dirichlet-to-Neumann map in inverse scattering problems using integral equation methods, Advances in Computational Mathematics, 36(2), 279-297, 2012.
53. J.J.Liu, H.L.Xu, Reconstruction of biologic tissue conductivity from noisy magnetic field by integral equation method, Applied Mathematics and Computation, 218(6), 2647-2660, 2011.
52. B.Wu, J.J.Liu, Conditional stability and uniqueness for determining two coefficients in a hyperbolic-parabolic system, Inverse Problems, 27(7), 075013, 2011.
51. B.Wu, J.J.Liu, A global in time existence and uniqueness result for an integrodifferential hyperbolic inverse problem with memory effect, J. Math. Anal. Appl., 373(2), 585-604, 2011.
50. J.J.Liu, P.A.Krutitskii, M.Sini, Numerical solution of the scattering problem for acoustic waves by a two-sided crack in 2-dimensional space, J. Comput. Math., 29(2), 141-166, 2011.
49. J.J.Liu, M.Yamamoto, A backward problem for the time-fractional diffusion equation, Applicable Analysis, 89(11), 1769-1788, 2010.
48. J.J.Liu, J.K.Seo, E.J.Woo, A posteriorierror estimate and convergence analysis for conductivity image reconstruction in MREIT, SIAM J. Appl. Math., 70(8), 2883-2903, 2010.
47. H.L.Xu, J.J.Liu, Stable numerical differentiation for the second order derivatives, Advances in Computational Mathematics, 33(4), 431-447, 2010.
46. H.B.Wang, J.J.Liu, On the reconstruction of Dirichlet-to-Neumann map in inverse scattering problems with stability estimates, Science China Mathematics, 53(8), 2069-2084, 2010.
45. J.J.Liu, M.Sini, Reconstruction of cracks of different types from far field measurements, Mathematical Methods in the Applied Sciences, 33(8), 950-973, 2010.
44. Z.W.Wang, J.J.Liu, New model function methods for determining regularization parameters in linear inverse problems, Appl. Numer. Math., 59(10), 2489-2506, 2009.
43. J.J.Liu, M.Sini, On the accuracy of the numerical detection of complex obstacles from far field data using the probe method, SIAM J. Sci. Comput., 31(4), 2665-2687, 2009.
42. J.Cheng, J.J.Liu, G.Nakamura, S.Z.Wang, Recovery of multiple obstacles by probe method, Quart. Appl. Math., 67(2), 221-247, 2009.
41. J.J.Liu, R.Potthast, On the duality of the potential method and point source method in inverse scattering problems, J. Integral Equations and Applications, 21(2), 297-315, 2009.
40. Y.Daido, Y.Lei, J.J.Liu, G.Nakamura, Numerical implementations of dynamical probe method for non-stationary heat equation, Applied Mathematics and Computation, 211(2), 510-521, 2009.
39. Q.Chen, B.Z.Huang, J.J.Liu, An inverse problem for conductivity imaging with regularization, Jishuan Shuxue, 31(1), 51-64, 2009.
38. P.A.Krutitskii, J.J.Liu, M.Sini, Reconstruction of complex cracks by far field measurements, 6th Int. Conf. Inverse Problems in Engineering: Theory and Practice, J. Physics: Conference Series, 135, doi:10.1088/1742-6596/135/1/012056, 2008.
37. J.Cheng, J.J.Liu, A quasi Tikhonov regularization for 2-dimensional backward heat problem by fundamental solution, Inverse Problems, 24(6), 065012, 2008.
36. J.K.Seo, S.W.Kim, S.Kim, J.J.Liu, E.J.Woo, K.Jeon, C.O.Lee, Local harmonic B_z algorithm with domain decomposition in MREIT: computer simulation, IEEE Trans. Med. Imag., 27(12), 1754-1761, 2008.
35. J.J.Liu, M.Ni, A model function method for determining the regularizing parameter in potential approach for the recovery of scattered wave, Appl. Numer. Math., 58(8), 1113-1128, 2008.
34. J.X.Su, J.J.Liu, A splitting algorithm for the coefficient inversion of1-dimensional parabolic equation, Jisuan Shuxue, 30(1), 99-112, 2008.
33. H.B.Wang, J.J.Liu, Numerical realization of probe method for multiple obstacle, Jisuan Shuxue, 29(2), 189-202, 2007.
32. J.J.Liu, J.K.Seo, E.J.Woo, On the conductivity imagining by MREIT: available resolution and noise effect, Inverse Problems in Applied Science-Towards Breakthrough, J. Physics: Conference Series, 73, 2007.
31. Li Gongsheng, Cheng Jin, Yao De, Liu Hongliang, Liu Jijun, One-dimensional equilibrium model and source parameter determination for soil-column experiment, Applied Mathematics and Computation, 190(2), 1365-1374, 2007.
30. H.B.Wang, J.J.Liu, Numerical solution for the Helmholtz equation with mixed boundary condition, Numerical Mathematics A Journal of Chinese Universities, 16(3), 203-214, 2007.
29. J.J.Liu, J.K.Seo, M.Sini, E.J.Woo, On the convergence of the harmonic B_z algorithm in magnetic resonance electrical impedance tomography, SIAM J. Appl. Math., 67(5), 1259-1282, 2007.
28. J.J.Liu, G.Nakamura, M.Sini, Reconstruction of the shape and surface impedance from acoustic scattering data for arbitrary cylinder, SIAM J. Appl. Math., 67(4), 1124-1146, 2007.
27. F.B.Hassen, J.J.Liu, R.Potthast, On source analysis by wave splitting with applications in inverse scattering of multiple obstacles, J. Comput. Math., 25(3), 266-281, 2007.
26. J.J.Liu, G.Nakamura, R.Potthast, A new approach and improved error analysis for reconstructing the scattered wave by the point source method, J. Comput. Math., 25(2), 113-130, 2007.
25. M.Yuan, J.J.Liu, Numerical realization of probe method for 2-D inverse scattering, Jisuan Shuxue, 28(2), 189-200, 2006.
24. Q.Cheng, J.J.Liu, Solving an inverse parabolic problem by optimization from final measurement data, J. Comput. Appl. Math., 193(1), 183-203, 2006.
23. J.J.Liu, H.C.Pyo, J.K.Seo, E.J.Woo, Convergence properties and stability issues in the MREIT algorithm, Contemporary Mathematics, AMS, 408, 201-218, 2006.
22. J.J.Liu, On uniqueness and linearization of an inverse electromagnetic scattering problem, Applied Mathematics and Computation, 171(1), 406-419, 2005.
21. J.X.Su, J.J.Liu, Reconstruction of density and wave velocity from reflection and transmission data, J. Southeast University (English Edition), 21(2), 233-238, 2005.
20. J.J.Liu, Inverse scattering problems by singular source methods, Numerical Mathematics A Journal of Chinese Universities, 14(3), 193-207, 2005.
19. H.Li, J.J.Liu, Solving backward heat problem by Morozov discrepancy principle and conditional stability, Numerical Mathematics A Journal of Chinese Universities, 14(2), 180-192, 2005.
18. J.Cheng, J.J.Liu, G.Nakamura, The numerical realization of the probe method for the inverse scattering problems from the near field data, Inverse Problems, 21(3), 839-855, 2005.
17. J.J.Liu, Determination of Dirichlet-to-Neumann map for a mixed boundary problem, Applied Mathematics and Computation, 161(3), 843-864, 2005.
16. J.J.Liu, J.K.Seo, On stability for a translated obstacle with impedance boundary, Nonlinear Analysis-TMA, 59(5), 731-744, 2004.
15. J.J.Liu, J.Cheng, G.Nakamura, Reconstruction of scattered field from far-field by regularization, J. Comput. Math., 22(3), 389-402, 2004.
14. J.Cheng, J.J.Liu, G.Nakamura, Recovery of the shape of an obstacle and the boundary impedance from the far-field pattern, J. Math. Kyoto Univer., 43(1), 165-186, 2003.
13. J.J.Liu, Continuous dependance for a backward parabolic problem, J. Partial Differential Equations, 16(3), 211-222, 2003.
12. J.J.Liu, D.J.Lou, On stability and regularization for backward heat equation, Chinese Annals of Mathematics, 24(1), Ser.B, 35-44, 2003.
11. Liu Jijun, The 3-layered explicit difference scheme for 2-D heat equation, Applied Mathematics and Mechanics, 24(5), 605-613, 2003.
10. J.Cheng, J.J.Liu, G.Nakamura, Inverse scattering for multiple obstacles, Theoretical and Applied Mechanics Japan, 51, 401-410, 2002.
9. J.J.Liu, Numerical solutions of forward and backward heat equations, J. Computational and Applied Mathematics, 145(2), 459-482, 2002.
8. Jijun Liu, Linearlization ill-posedness for 2.5-d wave equation inversion model, Acta Mathematicae Applicatae Sinica, English Ser., 18(2), 219-230, 2002.
7. Liu Jijun, Cheng Jin, G. Nakamura, Reconstruction and uniqueness of an inverse scattering problem with impedance boundary, Science in China, Ser.A, 45(11), 1408-1419, 2002.
6. Liu Jijun, Determination of temperature field for backward heat equation, Comm. Korea Math. Society, 16(3), 385-397, 2001.
5. Liu Jijun, Recovery of boundary impedance coefficient in 2-D media, Chinese J. Numer. Math. Appl., 23(2), 111-120, 2001.
4. Liu Jijun, On the ill-posedness of the 2.5-d linearized density inversion model, Inverse Problems, 16(6), 1861-1874, 2000.
3. Liu Jijun, Inverse scattering for the problem with impedance-type boundary, J. Partial Differential Equations, 13(3), 279-288, 2000.
2. Liu Jijun, Wang Yuanming, Reconstruction of mobilities for electrons and holes in semiconductors, J. Partial Differential Equations, 12(4), 289-300, 1999.
1. Liu Jijun, Wang Yuanming, On uniqueness of an inverse problem for a 1-d wave equation from transmission data, SIAM J. Appl. Math., 57(1), 195-204, 1997.
学术专著：
1. 刘继军，不适定问题的正则化方法和应用，信息与计算科学丛书，Vol.36, 科学出版社，2005。
2. 刘继军，现代数值计算方法，信息与计算科学丛书，Vol.47, 科学出版社，2009。