主要研究方向: （1）等离子共振分析、隐形设计、超分辨成像 [3] Z. Q. Miao and G. H. Zheng, On uniqueness and nonuniqueness for potential reconstruction in quantum fields from one measurement II. the non-radial case, (2019), (Submitted). [2] G. H. Zheng and Z. Q. Miao, On uniqueness and nonuniqueness for potential reconstruction in quantum fields from one measurement, (2019), (Submitted). [1] G. H. Zheng, Mathematical analysis of plasmonic resonance for 2-D photonic crystal, J. Differential Equations, 266 (2019), 5095–5117. （2）贝叶斯统计反问题、偏微分方程反问题 [19] X. Y. Song, G. H. Zheng and L. J. Jiang, Variational Bayesian inversion for reaction coefficient in space-time nonlocal diffusion equations, (2019), (Submitted). [18] M. H. Ding and G. H. Zheng, Determination of the reaction coefficient in a time dependent nonlocal diffusion process, (2019), (Submitted). [17] G. H. Zheng and M. H. Ding, Identification of the degradation coefficient for an anomalous diffusion process in hydrology, Inverse Problems (2019) (Accepted). [16] G. H. Zheng, Solving the backward problem in Riesz-Feller fractional diffusion by a new nonlocal regularization method, Appl. Numer. Math., 135 (2019), 99–128. [15] X. Y. Song, G. H. Zheng and L. J. Jiang, Identification of the reaction coefficient in time fractional diffusion equations, J. Comput. Appl. Math., 345 (2019), 295–309. [14] G. H. Zheng and Q. G. Zhang, Solving the backward problem for space-fractional diffusion equation by a fractional Tikhonov regularization method, Math. Comput. Simulation, 148 (2018), 37–47. [13] G. H. Zheng and Q. G. Zhang, Determining the initial distribution in space-fractional diffusion by a negative exponential regularization method, Inverse Problems in Science and Engineering, (2016). [12] G. H. Zheng and Q. G. Zhang, Recovering the initial distribution for space-fractional diffusion equation by a logarithmic regularization method. Appl. Math. Lett. 61 (2016), 143–148. [11] G. H. Zheng, Recover the solute concentration from source measurement and boundary data, Inverse Problems in Science and Engineering, 23 (2015), 1199-1221. [10] C. Shi, C. Wang, G. H. Zheng and T. Wei, A new a posteriori parameter choice strategy for the convolution regularization of the space-fractional backward diffusion problem, Journal of Computational and Applied Mathematics, 279 (2015), 233-248. [9] G. H. Zheng and T. Wei, Recover the source and initial value simultaneously in a parabolic equation, Inverse Problems, 30 (2014), 065013 (35pp). [8] H. Cheng, C. L. Fu, G. H. Zheng and J. Gao, A regularization for a Riesz-Feller space-fractional backward diffusion problem, Inverse Problems in Science and Engineering, 22 (2013), 860-872. [7] G. H. Zheng and T. Wei, A new regularization method for a Cauchy problem of the time fractional diffusion equation, Advances in Computational Mathematics, 36 (2012), 377-398. [6] G. H. Zheng and T. Wei, A new regularization method for the time fractional inverse advection-dispersion problem, SIAM Journal on Numerical Analysis, 49 (2011), 1972-1990. [5] G. H. Zheng and T. Wei, A new regularization method for solving a time fractional inverse diffusion problem, Journal of Mathematical Analysis and Applications, 378 (2011), 418-431. [4] G. H. Zheng and T. Wei, Spectral regularization method for a time fractional inverse diffusion problem, Applied Mathematics and Computation, 218 (2011), 396-405 [3] G. H. Zheng and T. Wei, Two regularization methods for solving a Riesz-Feller space-fractional backward diffusion problem, Inverse Problems, 26 (2010), 115017 (22pp). [2] G. H. Zheng and T. Wei, Spectral regularization method for a Cauchy problem of the time fractional advection-dispersion equation, Journal of Computational and Applied Mathematics, 233 (2010), 2631-2640. [1] G. H. Zheng and T. Wei, Spectral regularization method for the time fractional inverse advection-dispersion equation, Mathematics and Computers in Simulation, 81 (2010), 37-51. 博士研究生：丁明慧 硕士研究生：苗志强、王丽丽、孙泽军、姚远 (欢迎有一定数学基础，喜欢写程序，或者对概率统计有兴趣的学生报考我的研究生) 担任下列学术期刊的审稿人，并被国际反问题权威期刊《Inverse Problems》评为2016年 “Outstanding Reviewer Awards 2016”： Inverse Problems; Journal of Inverse and Ill-Posed Problems; Inverse Problems in Science and Engineering; Journal of Physics A: Mathematical and Theoretical; Applied Numerical Mathematics; Mathematical Methods in the Applied Sciences; Mathematics and Computers in Simulation; Journal of Engineering Mathematics; Acta Mathematica Scientia; |
