Publications

Preprint(s)

  1. Phuong M. Nguyen, Loc H. Nguyen, and Huong Vu, A robust approach with numerical demonstrations for the inverse scattering problem using a Carleman contraction map, preprint arXiv:2404.04145, 2024.
  2. Ray Abney, Thuy T. Le, Loc H. Nguyen, and Cam Peters, A Carleman-Picard approach for reconstructing zero-order coefficients in parabolic equations with limited data, preprint ArXiv:2309:14599, 2023.

Book

  1. Dinh-Liem Nguyen, L. H. Nguyen, and Thi-Phong Nguyen, Advances in Inverse problems for Partial Differential Equations, Volume 784, American Mathematical Society, 2023. (edited book)
  2. H. Ammari, J. Garnier, H. Kang, L. H. Nguyen and L. Seppecher, Multi-Wave Medical Imaging: Mathematical Modelling and Imaging Reconstruction. Modelling and Simulation in Medical Imaging, Volume 2, World Scientific, London, 2017. (link)

Journal papers

  1. Trong D. Dang, Loc H. Nguyen, and Huong T. Vu, Determining initial conditions for nonlinear hyperbolic equations with time dimensional reduction and the Carleman contraction, preprint arXiv:2312.01179, to appear on Inverse Problems,2024.
  2. Thuy T. Le, Linh V. Nguyen, Loc H. Nguyen, and Hyunha Park, The time dimensional reduction method to determine the initial conditions without the knowledge of damping coefficients, to Computers and Mathematics with Applications, 166(2024), 77-90.
  3. H. P. Le, T. T. Le and L. H. Nguyen, The Carleman convexification method for Hamilton-Jacobi equations on the whole space, Computers and Mathematics with Applications, 159(2024), 173–185.
  4. A. Abhishek, T. T Le, L. H. Nguyen, T. Khan, The Carleman-Newton method to globally reconstruct the initial condition for nonlinear parabolic equations, Journal of Computational and Applied Mathematics, 445(2024), 115827.
  5. Dinh-Nho Hào, Thuy T. Le and Loc H. Nguyen, The Fourier-based dimensional reduction method for solving a nonlinear inverse heat conduction problem with limited boundary data, Communications in Nonlinear Science and Numerical Simulation, 128:107679, 2024.
  6. Phuong M. Nguyen, Thuy T. Le, Loc H. Nguyen, and Michael V. Klibanov, Numerical differentiation by the polynomial-exponential basis,Journal of Applied and Industrial Mathematics, 17 (2023), 928-942.
  7. Thuy T. Le, Vo A. Khoa, Michael V. Klibanov, Loc H. Nguyen, Grant Bidney, and Vasily Astratov, Numerical verification of the convexification method for a frequency-dependent inverse scattering problem with experimental data, Journal of Applied and Industrial Mathematics, 17 (2023), 908-927.
  8. M. V. Klibanov, J. Li, L. H. Nguyen, V. G. Romanov, Z. Yang, Convexification Numerical Method for a Coefficient Inverse Problem for the Riemannian Radiative Transfer Equation, SIAM Journal on Imaging Sciences, 16 (2023), 1762-1790.
  9. L.H. Nguyen, The Carleman contraction mapping method for quasilinear elliptic equations with over-determined boundary data, Acta Mathematica Vietnamica, 48(2023), 401-422.
  10. M. V. Klibanov, J. Li, L. H. Nguyen and Z. Yang, Convexification numerical method for a coefficient inverse problem for the radiative transport equation, SIAM Journal on Imaging Sciences, 16 (2023), 35-63. 
  11. V.A. Khoa, M. V. Klibanov, W. G. Powell and L. H. Nguyen, Numerical reconstruction for 3D nonlinear SAR imaging via a version of the convexification method. In D-L Nguyen, L. H. Nguyen, and T-P. Nguyen, editors, Advances in Inverse problems for Partial Differential Equations, volume 784, pages 145-167, Contemporary Mathematics, American Mathematical Society, 2023.
  12. L. H. Nguyen and H. T. Vu. Reconstructing a space-dependent source term via the quasi-reversibility method. In D-L Nguyen, L. H. Nguyen, and T-P. Nguyen, editors, Advances in Inverse problems for Partial Differential Equations, volume 748, pages 103-118. Contemporary Mathematics, American Mathematical Society, 2023.
  13. D-L Nguyen, L. H. Nguyen and T. Truong, The Carleman-based contraction principle to reconstruct the potential of nonlinear hyperbolic equations, Computers and Mathematics with Applications, 128(2022), 239-248.
  14. T. T. Le, L. H. Nguyen and H. V. Tran, A Carleman-based numerical method for quasilinear elliptic equations with over-determined boundary data and applications, Computers and Mathematics with Applications, 125(2022), 13-24.
  15. T.T. Le and L. H. Nguyen, The gradient descent method for the convexification to solve boundary value problems of quasi-linear PDEs and a coefficient inverse problem, Journal of Scientific Computing, 91:74, 2022.
  16. T. Le, Michael V. Klibanov, L. H. Nguyen, A. Sullivan and L. Nguyen, Carleman contraction mapping for a 1D inverse scattering problem with experimental time-dependent data, Inverse Problems, 38(2022), 045002.
  17. L. H. Nguyen and M. V. Klibanov, Carleman estimates and the contraction principle for an inverse source problem for nonlinear hyperbolic equations, Inverse Problems, 38 (2022), 035009.
  18. M. V. Klibanov, L. H. Nguyen and H. V. Tran, Numerical viscosity solutions to Hamilton-Jacobi equations via a Carleman estimate and the convexification method, Journal of Computational Physics, 451(2022), 110828. 
  19. T. T. Le and L. H. Nguyen, A convergent numerical method to recover the initial condition of nonlinear parabolic equations from lateral Cauchy data, Journal of Ill-posed and Inverse Problems, 30, p 256-286, 2022.
  20. M. V. Klibanov, T. T. Le, L. H. Nguyen, A. Sullivan, and L. Nguyen, Convexification-based globally convergent numerical method for a 1D coefficient inverse problem with experimental data, Inverse Problems and Imaging, 16, p. 1579-1618, 2022.
  21. M. V. Klibanov, V. A. Khoa, A. V. Smirnov, L. H. Nguyen, G. W. Bidney, L. Nguyen, A. J. Sullivan and N. V. Astrativ, Convexification inversion method for nonlinear SAR imaging with experimentally collected data, J. Applied and Industrial Mathematics, 15(2021), p. 413-436.
  22. T. T. Le, L. H. Nguyen, T-P. Nguyen and W. Powell, The quasi-reversibility method to numerically solve an inverse source problem for hyperbolic equations, Journal of Scientific Computing 87:90, 2021.
  23. Vo Anh Khoa, Grant W. Bidney, Michael V. Klibanov, L. H. Nguyen, Lam H. Nguyen, Anders J. Sullivan, Vasily N. Astratov, An inverse problem of a simultaneous reconstruction of the dielectric constant and conductivity from experimental backscattering data, Inverse Problems in Science and Engineering 29, 712-735, 2021.
  24. L. H. Nguyen, A new algorithm to determine the creation or depletion term of parabolic equations from boundary measurements, Computers and Mathematics with Applications 80(2020), 2135-2149, https://doi.org/10.1016/j.camwa.2020.09.010.
  25. M. V. Klibanov, T. T. Le and L. H. Nguyen, Convergent numerical method for a linearized travel time tomography problem with incomplete data, SIAM Journal on Scientific Computing 42(2020) B1173-B1192.
  26. A. Smirnov, M. V. Klibanov and L. H. Nguyen, Convexification for a 1D hyperbolic coefficient inverse problem with single measurement data, Inverse Problems and Imaging, 14(2020), 913-938 (link).
  27. Vo Anh Khoa , Grant W. Bidney, Michael V. Klibanov, L. H. Nguyen, Lam H. Nguyen , Anders J. Sullivan , Vasily N. Astratov, Convexification and experimental data for a 3D inverse scattering problem with the moving point source, Inverse Problems, 36(2020), 085007 (link).
  28. V. A. Khoa, M. V. Klibanov and L. H. Nguyen, Convexification for a 3D inverse scattering problem with the moving point source, SIAM Journal on Imaging Sciences, 13(2020), 871-904 (link).
  29. P. M. Nguyen and L. H. Nguyen, A numerical method for an inverse source problem for parabolic equations and its application to a coefficient inverse problem, Journal of Ill-posed and Inverse Problems, 38(2020), 232-339 (link).
  30. Q. Li and L. H. Nguyen, Recovering the initial condition of parabolic equations from lateral Cauchy data via the quasi-reversibility method, Inverse Problems in Science and Engineering, 28 (2020), 580-598 (link).
  31. A. Smirnov, M. V. Klibanov and L. H. Nguyen, On an inverse source problem for the full radiative transfer equation with incomplete data, SIAM Journal on Scientific Computing, SIAM J. Sci. Comput., 41(2019), B929–B952.
  32. L. H. Nguyen, Q. Li and M. Klibanov, A convergent numerical method for a multi-frequency inverse source problem in inhomogeneous media, Inverse Problems and Imaging, 13(2019), 1067-1094. (link).
  33. M.V. Klibanov and L. H. Nguyen, PDE-based numerical method for a limited angle X-ray tomography, Inverse Problems, 35(2019), 045009 (pdf).
  34. L. H. Nguyen, An inverse space-dependent source problem for hyperbolic equations and the Lipschitz-like convergence of the quasi-reversibility method, Inverse Problems, 35(2019), 035007 (pdf).
  35. M.V. Klibanov, D.-L. Nguyen and L. H. Nguyen, A coefficient inverse problem with a single measurement of phaseless scattering data, SIAM Journal of Applied Mathematics, 79(2019), 1-27 (pdf).
  36. M.V. Klibanov, N. Koshev, D.-L. Nguyen, L. H. Nguyen, A. Brettin and V. Astratov, A numerical method to solve a phaseless coefficient inverse problem from a single measurement of experimental data, SIAM Journal on Imaging Sciences, 11(2018), 2339–2367 (pdf).
  37. M. Klibanov, D.-L. Nguyen, L. H. Nguyen and H. Liu, A globally convergent numerical method for a 3D coefficient inverse problem with a single measurement of multi-frequency data, Inverse Problems and Imaging, 12(2018), p. 493-523 (pdf).
  38. D-L. Nguyen, M. Klibanov, L. H. Nguyen and M. Fiddy, Imaging of buried objects from multi-frequency experimental data using a globally convergent inversion method, Inverse and Ill-posed Problems, 26(2018), p. 501-522 (pdf).
  39. A. E. Kolesov, M. V. Klibanov, L. H. Nguyen, D.-L. Nguyen and N. T. Thanh, Single measurement experimental data for an inverse medium problem inverted by a multi-frequency globally convergent numerical method, Applied Numerical Mathematics, 120(2017), p. 176-196. (pdf)
  40. D.-L. Nguyen, M. V. Klibanov, L. H. Nguyen, A. E. Kolesov, M. A. Fiddy and H. Liu, Numerical Solution of a Coefficient Inverse Problem with Multi-Frequency Experimental Raw Data by a Globally Convergent Algorithm, Journal of Computational Physics, 345(2017), p. 17-32. (pdf)
  41. H. Ammari, L. Giovangigli, L. H. Nguyen and J.K. Seo, Admittivity imaging from multi-frequency micro-electrical impedance tomography, Journal of Mathematical Analysis and Applications 449(2017), p. 1601-1618 (pdf).
  42. Michael Klibanov, L. H. Nguyen, Lam Nguyen and Anders Sullivan, A globally convergent numerical method for a 1-d inverse medium problem with experimental data, Inverse Problems and Imaging 10(2016), p. 1057-1085 (pdf).
  43. Michael Klibanov, L. H. Nguyen, and Kejia Pan, Nanostructures imaging via numerical solution of a 3-d inverse scattering problem without the phase information, Applied Numerical Mathematics, 110(2016), p. 190-203 (pdf).
  44. Hoai-Minh Nguyen and L. H. Nguyen, Localized and complete resonance in plasmonic structures, ESAIM: Mathematical Modelling and Numerical Analysis, 49(2015), p.741-754. (pdf)
  45. Hoai-Minh Nguyen and L. H. Nguyen, Cloaking using complementary media for the Helmholtz equation and a three spheres inequality for second order elliptic equations, Trans. Amer. Math. Soc. Ser. B, 2(2015), p. 93-112 (pdf).
  46. H. Ammari, L. H. Nguyen and L. Seppecher, Reconstruction and stability in acousto-optic imaging for absorption maps with bounded variation, Journal of Functional Analysis, 276 (2014), p. 4361-4398 (pdf).
  47. H. Ammari, E. Bossy, J. Garnier, L. H. Nguyen and L. Seppecher, A reconstruction algorithm for ultrasound-modulated optical tomography, Proceedings of the American Mathematical Society, 142 (2014), p. 3221-3236 (pdf).
  48. H. Ammari, J. Garnier, L. H. Nguyen and L. Seppecher, Reconstruction of a piecewise smooth absorption coefficient by an acousto-optic process, Communications in Partial Differential Equations, 38 (2013), p. 1737-1762,  (pdf)
  49. H. Ammari, J. Garnier, L. H. Nguyen and W. Jing, Quantitative thermo-acoustic imaging: An exact reconstruction formula, Journal of Differential Equations, 254(2013),p. 1375-1395. (pdf)
  50. Duong Minh Duc, L. H. Nguyen and Luc Nguyen, Existence of multiple solutions to elliptic equations satisfying a global eigenvalue-crossing condition, Electron. J. Differential Equations, 2013 (2013), No. 145, p. 1-24. (pdf)
  51. G.W. Milton and L. H. Nguyen, Bounds on the volume fraction of 2-phase, 2-dimensional elastic bodies and on (stress, strain) pairs in composites, Comptes Rendus Mecanique, 340(2012), p. 193-204. (pdf)
  52. L. H. Nguyen and K. Schmitt, Nonlinear elliptic Dirichlet and no-flux boundary value problems, Annals of the University of Bucharest, 3(LXI)(2012), p. 201-217 (pdf).
  53. L. H. Nguyen and K. Schmitt, Bernstein-Nagumo conditions and solutions to nonlinear differential inequalities, Nonlinear Analysis: Theory, Methods & Applications, 75(2012), p. 4664-4671 (pdf).
  54. L. H. Nguyen and K. Schmitt, Applications of sub-supersolution theorems to singular nonlinear elliptic problems, Advanced Nonlinear Studies, 11(2011), p. 493-524 (pdf).
  55. L. H. Nguyen and K. Schmitt, Boundary value problems for singular elliptic equations, Rocky Mountain J. Math., 41(2011), p. 555-572 (pdf).
  56. L. H. Nguyen and K. Schmitt, On positive solutions of quasilinear elliptic equations, Differential and Integral Equations, 22(2009), p. 829-842, (pdf).
  57. D. M. Duc, L. H. Nguyen and L. L. Phi. Nonlinear versions of Stampacchia and Lax-Milgram theorems and applications to p-Laplace equations, Nonlinear Analysis: Theory, Method & Applications, 68(2008), p. 925-931, (pdf)
  58. D. M. Duc, L. H. Nguyen and P. V. Tuoc, Generalized zeros of operators and applications, Vietnam J. Math., 32 SI (2004), p. 87-96. (pdf)
  59. D. M. Duc, L. H. Nguyen and P. V. Tuoc, Topological degree for a class of operators and applications, Nonlinear Analysis: Theory, Method & Applications, 57(2004), p. 505-518 (pdf).
 
  • Ph.D. Thesis: Existence of Solutions to Nonlinear Elliptic Equations, University of Utah (pdf).  Advisor: Klaus Schmitt.