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Inverse Problems:


1. Basic Theory + Algorithms:


  1. Junxiong Jia, Qian Zhao, Zongben Xu, Deyu Meng, Yee Leung, Variational Bayes' approach for functions and applications to some inverse problems, SIAM Journal on Scientific Computing, 43(1), A355-A383, 2021. PDF (arXiv) PDF (Sci-Hub)
  2. Junxiong Jia, Jigen Peng, Jinghuai Gao, Posterior contraction for empirical Bayesian approach to inverse problems under non-diagonal assumption,  Inverse Problems & Imaging,15(2): 201-228​​​​​​​, 2021. PDF (arXiv) PDF(Sci-Hub)
  3. Changlong Wang, Junxiong Jia, Jigen Peng, Shoujin Lin, A new sparse recovery method for the inverse acoustic scattering problem, Acta Mathematicae Applicatae Sinica, English Series (A special issue for IP), 31(1), 49-66, 2020. PDF
  4. Xiaohua Jing, Junxiong Jia, Jigen Peng, Well-posedness for a nonlocal nonlinear diffusion equation and applications to inverse problems, Applicable Analysis, 99(15), 2609-2623, 2020. PDF
  5. Junxiong Jia, Bangyu Wu, Jigen Peng, Jinghuai Gao, Recursive linearization method for inverse medium scattering problems with complex mixture Gaussian error learning,  Inverse Problems, 35(7),​​​​​​​ 075003, 2019. PDF(arXiv)
  6. Yuanxiang Zhang, Junxiong Jia, Liang Yan, Bayesian approach to a nonlinear inverse problem for time-space fractional diffusion equation, Inverse Problems, 34 (12), 125002, 2018. PDF(2018年度Inverse Problems编辑推荐的亮点文章)
  7. Angang Cui, Jigen Peng, Haiyang Li, Meng Wen, Junxiong Jia, Iterative thresholding algorithm based on non-convex method for modified l(p)-norm regularization minimization, Journal of Computational and Applied Mathematics, 347, 137--180, 2018.
  8. Junxiong Jia, Shigang Yue, Jigen Peng, Jinghuai Gao, Infinite-dimensional Bayesian approach for inverse scattering problems of a fractional Helmholtz equation, Journal of Functional Analysis, 275(9), 2299--2332, 2018. PDF

  9. Junxiong Jia, Jigen Peng, Jinghuai Gao and Yujiao Li, Backward problem for a time-space fractional diffusion equationInverse Problems & Imaging, 12 (2), 773--799, 2018.  PDF

  10. Junxiong Jia, Bangyu Wu, A Carleman estimate of some anisotropic space-fractional diffusion equations, Applied Mathematics Letters, 80, 1--7, 2018. PDF

  11. Junxiong Jia, Jigen Peng, Jiaqing Yang, Harnack's inequality for a space-time fractional diffusion equation and applications to an inverse source problem,  Journal of Differential Equations, 262 (8), 4415--4450, 2017. PDF

  12. Junxiong Jia, Jigen Peng and Jinghuai Gao, Bayesian approach to inverse problems for functions with a variable index Besov priorInverse Problems, 32 (8), 085006, 2016. PDF


2. Seismic Exploration


Journal Papers: 

  1. Bangyu Wu, Weirong Qiu, Junxiong Jia, Naihao Liu, Landslide susceptibility modeling using bagging based positive-unlabeled learning, IEEE Geoscience and Remote Sensing Letters, 2020.  PDF

  2. Bangyu Wu, Wenhao Xu, Bo Li, Junxiong Jia, Trapezoid coordinate finite difference modeling of acoustic wave propagation using the CPML boundary conditionJournal of Applied Geophysics, 168, 101-106, 2019. PDF

  3. Hui Yang, Junxiong Jia, Bangyu Wu, and Jinghuai Gao, Mini-batch optimized full waveform inversion with geological constrained gradient filtering, Journal of Applied Geophysics, 152, 9--16, 2018. PDF

Conference Papers :

  1. 邱维蓉, 吴帮玉, 贾骏雄. 基于正例和未标记样本的半监督集成学习方法在滑坡易发性预测中的应用, 中国石油学会2019年物探技术研讨会论文集, 2019.

  2. Bangyu Wu, Bo Li, Hui Yang and Junxiong Jia, 2018, Trapezoid grid finite difference for acoustic wave modeling, SEG 2018 Workshop: Seismic Imaging, Beijing, China, 12-14 November 2018.

  3. Bangyu Wu, Wenhao Xu, Junxiong Jia, Bo Li, Hui Yang, Haixia Zhao and Jinghuai Gao, 2018, Convolutional perfect matched layer boundary for trapezoid grid finite difference seismic modeling, SEG Technical Program Expanded Abstracts 2018, 3989-3993.
  4. Junxiong Jia, Qihang Sun, Bangyu Wu, Jigen Peng, A general local adaptive regularization inversion and its iterative solution, SEG Workshop: Full-waveform Inversion and Beyond, Extended Abstract, 2017.

Forward Problems:


1. Fractional Differential Equations


  1. Junxiong Jia, Kexue LiMaximum principles for a time-space fractional diffusion equationApplied Mathematics Letters, 62, 23--28, 2016. PDF
  2. Junxiong Jia, Jigen Peng, Kexue Li, Well posedness of abstract distributed order fractional diffusion equationsCommunications on Pure & Applied Analysis, 13 (2), 605--621, 2014. PDF
  3. Zhandong Mei, Jigen Peng, Junxiong JiaA new characteristic property of Mittag-Leffler functions and fractional cosine functionsStudia Mathematica, 220 (2), 119--140, 2014. PDF
  4. Kexue Li , Jigen Peng, Junxiong JiaCauchy problems for fractional differential equations with Riemann–Liouville fractional derivativesJournal of Functional Analysis, 263 (2), 476--510, 2012. PDF
  5. Kexue Li, Junxiong JiaExistence and uniqueness of mild solutions for abstract delay fractional differential equationsComputers & Mathematics with Applications, 62 (3), 1398--1404, 2011. PDF


2. Stochastic Differential Equations


  1. Kexue Li, Jigen Peng and Junxiong Jia, Explosive solutions of parabolic stochastic partial differential equations with Levy noise, Discrete and Continuous Dynamical Systems--Series A, 37(10), 5105--5125, 2017. PDF


3. Fluid Dynamic Equations


  1. Junxiong Jia, Optimal time decay of Navier-Stokes equations with low regularity initial data, Acta Mathematica Sinica, English Series, 34(5), 855--872, 2018. PDF
  2. Junxiong Jia, Jigen Peng, Kexue Li, On the decay and stability of global solutions to the 3D inhomogeneous MHD systemCommunications on Pure & Applied Analysis, 16 (3), 745--780, 2017. PDF
  3. Hermano Frid, Junxiong Jia, Ronghua Pan, Global smooth solutions in R-3 to short wave-long wave interactions systems for viscous magnetohydrodynamic fluidsJournal of Differential Equations, 262 (7), 4129--4173, 2017.  PDF
  4. Junxiong Jia, Jigen Peng, Jinghuai Gao, Well-posedness for compressible MHD systems with highly oscillating initial dataJournal of Mathematical Physics,  57, 081514, 2016. PDF
  5. Junxiong Jia, Jigen Peng, Optimal time decay rate for the compressible viscoelastic equations in critical spacesApplicable Analysis, 24, 1--21, 2016. PDF
  6. Junxiong Jia, Jigen Peng, Kexue Li, On the global well-posedness of a generalized 2D Boussinesq equation, NoDEA-Nonlinear Differential Equations and Applications, 22 (4), 911--945, 2015. PDF
  7. Junxiong Jia, Ronghua Pan, On isentropic approximations in compressible euler equationsJournal of Scientific Computing, 64 (3), 745--760, 2015. PDF
  8. Junxiong Jia, Jigen Peng, Zhandong Mei, Well-posedness and time-decay for compressible viscoelastic fluids in critical Besov spaceJournal of Mathematical Analysis and Applications, 418 (2), 638--675, 2014. PDF


Recently submitted manuscripts:


  1. Junxiong Jia, Yujiao Li, Jigen Peng, Inverse medium scattering problem for dispersion-dominated fractional Helmholtz equation, 2021
  2. Junxiong Jia, Deyu Meng, Stein variational gradient descent on infinite-dimensional space and applications to statistical inverse problems, 2021. PDF