Recent Publications by Hongyu Liu 

 (Click on the title of the paper to get the published journal version, and click on arXiv/PDF to get a preprint version)


  1. Hongjie Li and Hongyu Liu
    On anomalous localized resonance and plasmonic cloaking at optical frequencies
     arXiv
  2. Jingzhi Li, Hongyu Liu and Hongpeng Sun
    On an inverse elastic wave imaging scheme for nearly incompressible materials
     arXiv
  3. Jingzhi Li, Hongyu Liu and Hongpeng Sun
    On a gesture-computing technique using electromagnetic waves
    Inverse Problems and Imaging, to appear  arXiv
  4. Jingzhi Li, Xiaofei Li and Hongyu Liu
    Reconstruction via the intrinsic geometric structures of interior transmission eigenfunctioins
     arXiv
  5. Eemeli Blasten and Hongyu Liu
    Recovering piecewise-constant refractive indices by a single far-field pattern
     arXiv
  6. Yukun Guo, Jingzhi Li, Hongyu Liu and Xianchao Wang
    Two gesture-computing approaches by using electromagnetic waves
     arXiv
  7. Hongjie Li, Jinhong Li and Hongyu Liu
    On novel elastic structures inducing plasmonic resonances with finite frequencies and cloaking due to anomalous localized resonance
     arXiv
  8. Eemeli Blasten, Xiaofei Li, Hongyu Liu and Yuliang Wang
    On vanishing and localizing of transmission eigenfunctions near singular points: a numerical study
    Inverse Problems, 33 (2017), 105001. arXiv
  9. Youjun Deng, Hongjie Li and Hongyu Liu
    On spectral properties of Neumann-Poincare operator and plasmonic cloaking in 3D elastostatics
     arXiv
  10. Eemeli Blasten and Hongyu Liu
    On vanishing near corners of transmission eigenfunctions
    Journal of Functional Analysis, 273(2017), 3616--3632. arXiv
    Addendum
  11. Youjun Deng, Hongyu Liu and Gunther Uhlmann
    On an inverse boundary problem arising in brain imaging
     arXiv
  12. Jingzhi Li, Xiaofei Li, Hongyu Liu and Yuliang Wang
    Electromagnetic interior transmission eigenvalue problem for inhomogeneous media containing obstacles and its applications to near cloaking
    IMA Journal of Applied Mathematics, 82 (2017), 1013--1042. arXiv
  13. Eemeli Blasten and Hongyu Liu
    On corners scattering stably and stable shape determination by a single far-field pattern
     arXiv
  14. Hongyu Liu and Jingni Xiao
    On electromagnetic scattering from a penetrable corner
    SIAM J. Math. Anal., to appear  arXiv
  15. Xiaodong Liu and Hongyu Liu
    Recovery of an embedded obstacle and its surrounding medium by formally-determined scattering data
    Inverse Problems, 33 (2017), 065001.  arXiv
  16. Yujing Shi, Yueru Li, Shanqiang Li and Hongyu Liu
    State feedback design for nonlinear quadratic systems with randomly occurring actuator saturation
    International Journal of Control, Automation and Systems, 15 (2017), issue 3, pp. 1117--11124. PDF
  17. Deyue Zhang, Yukun Guo, Jingzhi Li and Hongyu Liu
    Locating multiple multipolar acoustic sources using the direct sampling method
    arXiv
  18. Xianchao Wang, Yukun Guo, Deyue Zhang and Hongyu Liu
    Fourier method for recovering acoustic sources from multi-frequency far-field data
    Inverse Problems, 33 (2017), 035001.
  19. Yukun Guo, Jingzhi Li, Hongyu Liu and Xianchao Wang
    Mathematical design of a novel input/instruction device using a moving emitter
    Inverse Problems, 33 (2017), 105009.  arXiv
  20. Jingzhi Li, Hongyu Liu and Yuliang Wang
    Recovering an electromagnetic obstacle by a few phaseless backscattering measurements
    Inverse Problems, 33 (2017), 035011.  arXiv
  21. Hongjie Li and Hongyu Liu
    On three-dimensional plasmon resoance in elastostatics
    Annali di Matematica Pura ed Applicata (AMPA), 196 (2017), issue 3, pp. 1113--1135. arXiv
  22. Xia Ji and Hongyu Liu
    On isotropic cloaking and inerior transmission eigenvalue problems
    European Journal of Applied Mathematics, to appear.  arXiv
  23. Hongyu Liu, Yuliang Wang and Shuhui Zhong
    Nearly non-scattering electromagnetic wave set and its application
    Zeitschrift fur Angewandte Mathematik und Physik (ZAMP), 68 (2017), 68:35.
  24. Hongyu Liu, Luca Rondi and Jingni Xiao
    Mosco convergence for H(curl) spaces, higher integrability for Maxwell's equations, and stability in direct and inverse EM scattering problems
    Journal of the European Mathematical Socieity (JEMS), to appear. arXiv
  25. Hongyu Liu, Yuliang Wang and Can Yang
    Mathematical design of a novel gesture-based instruction/input device using wave detection

    SIAM J. Imaging Sci., 9 (2016), no. 2, 822--841.  arXiv
  26. Hongjie Li and Hongyu Liu
    On anomalous localized resoance for the elastostatic system
    SIAM J. Math. Anal., 48 (5), 3322--3344, 2016. arXiv
  27. Xianchao Wang, Yuku Guo, Deyue Zhang and Hongyu Liu
    Fourier method for recoveirng acoustic sources from multi-frequency far-field data

    Inverse Problems, 33 (2017), 035001.

  28. Yukun Guo, Dietmar Homberg, Guanghui Hu, Jingzhi Li and Hongyu Liu
    A time-domain sampling method for inverse acoustic scattering problems
    J. Comput. Phys., 314 (2016), 647--660.
  29. Hongyu Liu and Jingni Xiao
    Decoupling elastic waves and its applications
    J. Differential Equations, 263 (2017), no. 8, 4442--4480.
    arXiv
  30. Youjun Deng, Hongyu Liu and Gunther Uhlmann
    Full and partial cloaking in electromagnetic scattering 
    Arch. Ration. Mech. Anal. (ARMA), Vol. 223, Issue 1, pp. 265--299, 2017. arXiv
  31. Kazunori Ando, Hyeonbae Kang and Hongyu Liu
    Plasmon resonance with finite frequencies: a validation of  the quasi-static approximation for diametrically small inclusions
    SIAM J. Appl. Math., 76 (2016), no. 2, 731--749. arXiv
  32. Hongyu Liu, Michele Petrini, Luca Rondi and Jingni Xiao
    Stable determination of sound-hard polyhedral scatterers by a minimal number of scattering measurements 
    J. Differential Equations, 262 (2017), no. 3, 1631--1670.  
    arXiv
  33. Youjun Deng, Hongyu Liu and Gunther Uhlmann
    On regularized full- and partial-cloaks in acoustic scattering
    Comm. Partial Differential Equations, vol. 42, 2017, issue 6, 821--851. arXiv  
  34. Hongyu Liu and Gunther Uhlmann
    Determining both sound speed and internal source in thermo- and photo-acoustic tomography

    Inverse Problems, 31 (2015) 105005. arXiv
  35. Guanghui Hu, Jingzhi Li, Hongyu Liu and Qi Wang
    A numerical study of complex reconstruction in inverse elastic scattering
    Comm. Comput. Phys., 19 (2016), no. 5, 1265--1286. PDF
  36. Jingzhi Li, Peijun Li, Hongyu Liu and Xiaodong Liu
    Recovering multiscale buried anomalies in a two-layered medium

    Inverse Problems, 31 (2015), 105006. PDF
  37. Hongjie Li, Jingzhi Li and Hongyu Liu
    On quasi-static cloaking due to anomalous localized resonance in R^3
    SIAM J. Appl. Math., 75 (2015), no. 3, 1245--1260. arXiv
  38. Jingzhi Li and Hongyu Liu
    Recovering a polyhedral obstacle by a few backscattering measurements

    J. Differential Equations, 259 (2015), no. 5, 2101--2120. arXiv
  39. Guanghui Hu and Hongyu Liu
    Nearly cloaking the elastic wave fields
    J. Math. Pures Appl. (9), 104 (2015), no. 6, 1045--1074.  arXiv
  40. Jingzhi Li, Hongyu Liu, Luca Rondi and Gunther Uhlmann
    Regularized transformation-optics cloaking for the Helmholtz equation: from partial cloak to full cloak
    Comm. Math. Phys., 335 (2015), 671--712. arXiv
  41. Hongyu Liu, Hongkai Zhao and Changjian Zou
    Determining scattering support of anisotropic acoustic mediums and obstacles
    Comm. Math. Sci., 13 (2015), no. 4, 987--1000. (Special issue in honor of the 70th birthday Prof. George Papanicolaou) PDF
  42. Jingzhi Li, Hongyu Liu and Hongpeng Sun
    Damping mechanisms for regularized transformation-acoustic cloaking
    Contemporary Mathematics, AMS, 615 (2014), 233—253. (Special issue in honor of the 60th birthday of Prof. Gunther Uhlmann) PDF
  43. Hongyu Liu and Gunther Uhlmann
    Regularized transformation-optics cloaking in acoustic and electromagnetic scattering
    Book chapter by Societe Mathematique de France
  44. Guanghui Hu, Jingzhi Li and Hongyu Liu
    Uniqueness in determining refractive indices by formally determined far-field data

    Applicable Analysis, 94 (2015), 1259--1269. arXiv
  45. Guagnhui Hu, Jingzhi Li, Hongyu Liu and Hongpeng Sun
    Inverse elastic scattering for multiscale rigid bodies with a single far-field pattern
    SIAM J. Imaging Sci., 7 (2014), 1799--1825. arXiv
  46. Gang Bao, Hongyu Liu and Jun Zou
    Nearly cloaking the full Maxwell equations: cloaking active contents with general conducting layers
    J. Math. Pures Appl. (9), 101 (2014), 716-733. arXiv
  47. Guanghui Hu, Jingzhi Li and Hongyu Liu
    Recovering complex elastic scatterers by a single far-field pattern
    J. Differential Equations, 257 (2014), 469-489.
  48. Gang Bao and Hongyu Liu
    Nearly cloaking the electromagnetic fields
    SIAM J. Appl. Math., 74 (2014), 724-742. arXiv
  49. Jingzhi Li, Hongyu Liu, Yuanchang Sun and Qi Wang
    Ground detection by a single electromagnetic far-field measurement
    J. Comput. Phys., 273 (2014), 472-487.
  50. Jingzhi Li, Hongyu Liu and Jun Zou
    Locating multiple multiscale acoustic scatterers

    SIAM Multiscale Model. Simul., 12 (2014), no. 3, 927-952.
  51. Jingzhi Li and Hongyu Liu
    Optimal shape for a nozzle design problem using an arbitrary Lagrangian-Eulerian finite element method
    J. Inverse Ill-posed Probl., 22 (2014), no. 1, 9-30.  
  52. Jingzhi Li, Hongyu Liu and Qi Wang
    Enhanced multilevel linear sampling methods for inverse scattering problems

    J. Comput. Phys., 257 (2014), 554-571.
  53. Hongyu Liu
    Schiffer’s conjecture, interior transmission eigenvalues and invisibility cloaking: singular problem vs. nonsingular problem
    Contemporary Mathematics, AMS, 598 (2013) (Special issue in honor of the 85th birthday of Prof. Sigurdur Helgason) arXiv