Preprints

Pr5. H.-M. Nguyen and M.-N. Tran, On the local null controllability of a viscous Burgers' system in finite time, submitted, https://arxiv.org/abs/2507.07442. 

Pr4.  H.-M. Nguyen, A short introduction to the control theory in finite-dimensional spaces, submitted, https://www.arxiv.org/abs/2505.02423. 

Pr3.  A. Dahmani, Y. Chitour, H.-M. Nguyen, C. Roman,  One dimensional wave equation with in-domain localized damping and Wentzell boundary conditions, submitted, https://arxiv.org/abs/2503.22439.

Pr2.  H.-M. Nguyen, Rapid and finite-time boundary stabilization of a KdV system,  submitted, https://arxiv.org/pdf/2409.11768.

Pr1.  H.-M. Nguyen, Rapid stabilization and finite time stabilization of the bilinear Schrödinger equation, submitted, https://arxiv.org/abs/2405.10002. 

List of Journal Publications

92. H.-M. Nguyen and E. Trelat, Turnpike property of linear quadratic control problems with unbounded control operators, to appear, 

Advances in Differential Equations, https://arxiv.org/abs/2506.01605. 

91. H.-M. Nguyen, Local controllability of the Korteweg-de Vries equation with the right Dirichlet control,  J. Differential Equations, 435 (2025)  113235. 

90.  A. Mallick and H.-M. Nguyen, Gagliardo-Nirenberg Inequalities in Fractional Coulomb-Sobolev spaces for Radial functions, Mathematische Zeitschrift,  to appear, https://doi.org/10.1007/s40306-018-0258-z. 

89.  H.-M. Nguyen, Stabilization of control systems associated with a strongly continuous group, ESAIM Control Optim. Calc. Var. , to appear, https://doi.org/10.1051/cocv/2024093. 

88.  J.-M. Coron, A. Koenig, and H.-M. Nguyen, Lack of local controllability for a water- tank system when the time is not large enough, Ann. Inst. H. Poincaré C Anal. Non Linéaire, 41 (2024) 1327-1365.  

87.  J.-M. Coron and H.-M. Nguyen,  On the optimal controllability time for hyperbolic systems with time-dependent coefficients, Ann. Inst. Fourier (Grenoble), to appear, hal-03158458. 

86.  Y. Chitour, H.-M. Nguyen, and C. Roman, Lyapunov functions for linear damped wave equations in one-dimensional space with dynamic boundary conditions, Automatica J. IFAC 167 (2024), Paper No. 111754. 

85.  Y. Chitour and H.-M. Nguyen, Exponential decay of solutions of damped wave equations in one dimensional space in the $L^p$ framework for various boundary conditions, ESAIM Control Optim. Calc. Var. 30 (2024), Paper No. 38, 26 pp. 

84.  J.-M. Coron, A. Koenig, and H.-M. Nguyen, On the small-time local controllability of a KdV system for critical lengths, J. Eur. Math. Soc. (JEMS) 26 (2024), no. 4, 1193--1253. 

83.  A. Mallick and H.-M. Nguyen, The Caffarelli-Kohn-Nirenberg inequalities for radial functions,  C. R. Math. Acad. Sci. Paris 361 (2023), 1175–1189.

82.  J. Fornerod and H.-M. Nguyen, The Weyl law of transmission eigenvalues and the completeness of generalized transmission eigenfunctions without complementing conditions, SIAM J. Math. Anal. 55 (2023), 3959–3999. 

81.  A. Mallick and H.-M. Nguyen, Gagliardo-Nirenberg and Caffarelli-Kohn-Nirenberg inter- polation inequalities associated with Sobolev-Coulomb spaces, J. Funct. Anal. 283 (2022), Paper No. 109662, 33 pp. link 

80. A. B. Movchan, N. V Movchan, I. S. Jones, G. M. Milton, and H.-M. Nguyen, Frontal waves and transmissions for temporal laminates and imperfect chiral interfaces, Philos. Trans. Roy. Soc. A 380 (2022), no. 2231, Paper No. 20210385, 27 pp.

79. J.-M. Coron and H.-M. Nguyen, Lyapunov functions and finite time stabilization in optimal time for homogeneous linear and quasilinear hyperbolic systems, Ann. Inst. H. Poincaré Anal. Non Linéaire 39 (2022), 1235–1260. link 

78. H.-M. Nguyen, A dependence of the cost of fast controls for the heat equation on the support of initial datum, SIAM J. Control Optim. 60 (2022), 530–544. link 

77. H.-M. Nguyen, Cloaking property of a plasmonic structure in doubly complementary media and three-sphere inequalities with partial data, SIAM J. Math. Anal. 54 (2022), 2040–2096. link 

76. J. Fornerod and H.-M. Nguyen, The completeness of the generalized eigenfunctions and an upper bound for the counting function of the transmission eigenvalue problem for Max- well equations, Res. Math. Sci. 9 (2022), Paper No. 6. 35P30 link 

75. H.-M. Nguyen Decay for the nonlinear KdV equations at critical lengths, J. Differential Equations 295 (2021), 249–291. link 

74. H.-M. Nguyen and Q. H. Nguyen, The Weyl law of transmission eigenvalues and the completeness of generalized transmission eigenfunctions, J. Funct. Anal. 281 (2021), Paper No. 109146, 37 pp.

73. F. Cakoni and H.-M. Nguyen, On the Discreteness of Transmission Eigenvalues for the Maxwell Equations, SIAM J. Math. Anal. 53 (2021), 888–913.

72. J.-M. Coron and H.-M. Nguyen, Null-controllability of linear hyperbolic systems in one dimensional space, Systems Control Lett. 148 (2021), 104851.

71. J.-M. Coron and H.-M. Nguyen, Finite-time stabilization in optimal time of homogeneous quasilinear hyperbolic systems in one dimensional space, ESAIM Control Optim. Calc. Var. 26 (2020), 24 pp.

70. H.-M. Nguyen and J. Van Schaftingen, Characterization of the traces on the boundary of functions in magnetic Sobolev spaces, Adv. Math. 371 (2020), 107246.

69. H.-M. Nguyen and S. Sil, Limiting absorption principle and well-posedness for the Max- well equations with anisotropic sign changing coefficients, Comm. Math. Phys. 379 (2020), 145–176.

68. H. Brezis and H.-M. Nguyen, Γ-convergence of non-local, non-convex functionals in one dimension, Commun. Contemp. Math. 22 (2020), 1950077, 27 pp.

67. A. Mallick and H.-M. Nguyen, Exponential integrability in the spirit of Moser-Trudinger’s inequalities of functions with finite non-local, non-convex energy, Pure Appl. Funct. Anal. 5 (2020), 1153–1165

66. H.-M. Nguyen, A. Pinamonti, M. Squassina, E. Vecchi, Some characterizations of ma- gnetic Sobolev spaces. Complex Var. Elliptic Equ. 65 (2020), 1104–1114.

65. H. Brezis and H.-M. Nguyen, Non-local, non-convex functionals converging to Sobolev norms, Nonlinear Anal., 191 (2020), 111626, 9pp.

64. H.-M. Nguyen and M. S. Vogelius, Approximate cloaking using transformation optics for acoustic and electromagnetic waves, Acta Math. Vietnam., 45 (2020) 261–280.

63. H.-M. Nguyen and M. Squassina, On Hardy and Caffarelli-Kohn-Nirenberg inequalities, J. d’Analyse Math., 139 (2019) 773–797.  

62. H.-M. Nguyen and X. L. Tran, Approximate cloaking for time-dependent Maxwell equa- tions via transformation optics, SIAM J. Math. Anal., 51 (2019), 4142–4171.

61. H.-M. Nguyen, The invisibility via anomalous localized resonance of a source for elec- tromagnetic waves, Res. Math. Sci 6 (2019), 32.

60. H.-M. Nguyen, Cloaking via anomalous localized resonance for doubly complementary media in the finite frequency regime, J. d’Analyse Math., 138 (2019), 157–184.

59. H.-M. Nguyen and T. Nguyen, Approximate cloaking for the heat equation via transfor- mation optics, Math. Eng. 1 (2019), 775–788.

58. H.-M. Nguyen, Cloaking using complementary media for electromagnetic waves, ESAIM Control Optim. Calc. Var. 25 (2019) 29.

57. H.-M. Nguyen and X. L. Tran, Approximate cloaking for electromagnetic waves via transformation optics : cloaking vs infinite energy, Math. Models Appl. Sci. 29 (2019), 1511–1552.

56. H.-M. Nguyen, Negative index materials : some mathematical perspectives, Acta Math. Vietnam., 44 (2019), 325–349

55. H.-M. Nguyen and M. Squassina, On anisotropic Sobolev spaces, Commun. Contemp. Math. 21 (2019), 1850017.  

54. J.-M. Coron and H.-M. Nguyen, Optimal time for the null-controllability of linear hy- perbolic systems in one dimensional space, SIAM J. Control Optim. 57 (2019), 1127–1156.

53. H.-M. Nguyen, Superlensing using complementary media and reflecting complementary media for electromagnetic waves, Adv. Nonlinear Anal. 7 (2018), 449–467.

52. H.-M. Nguyen and V. Vinoles, Electromagnetic wave propagation in dispersive metama- terials, C. R. Acad. Sci. Paris 356 (2018), 757–775.

51. H.-M. Nguyen and M. Squassina, Fractional Caffarelli-Kohn-Nirenberg inequalities, J. Funct. Anal. 274 (2018), 2661–2672.

50. H.-M. Nguyen, A. Pinamonti, M. Squassina, and E. Vecchi. New characterizations of magnetic Sobolev spaces, Adv. Nonlinear Anal. 7 (2018), 227–245.

49. H. Brezis and H.-M. Nguyen, Non-local functionals related to the total variation and connections with Image Processing, Ann. PDE 4 (2018), Art. 9, 77 pp.

48. H.-M. Nguyen and M. Squassina, Some remarks on rearrangement for nonlocal functio- nals, Nonlinear Anal. 162 (2017), 1–12.

47. H.-M. Nguyen and M. Squassina, Logarithmic Sobolev inequality revisited, C. R. Acad. Sci. Paris 355 (2017), 447–451.

46. H.-M. Nguyen and Q. H. Nguyen, On the discreteness of interior transmission eigenva- lues, Calc. Var. Partial Differential Equations 56 (2017), Art. 51, 38 pp.

45. H.-M. Nguyen, A refined estimate for the topological degree, C. R. Math. Acad. Sci. Paris 355 (2017), 1046–1049.

44. H.-M. Nguyen, Cloaking an arbitrary object via anomalous localized resonance : the cloak is independent of the object, SIAM J. Math. Anal. 49 (2017), 3208–3232.

43. E. Bonnetier and H.-M. Nguyen, Superlensing using hyperbolic metamaterials : the scalar case, J. Éc. polytech. Math. 4 (2017), 973–1003.

42. J.-M. Coron and H.-M. Nguyen, Null controllability and finite time stabilization for the heat equations with variable coefficients in space in one dimension via backstepping approach, Arch. Ration. Mech. Anal. 225 (2017), 993–1023.

41. H.-M. Nguyen, Negative index materials and their applications : recent mathematics progress, Chin. Ann. Math. Ser. B 38 (2017), 601–628.

40. H. Brezis and H.-M. Nguyen, Non-convex, non-local functionals converging to the total variation, C. R. Acad. Sci. Paris 355 (2017), 24–27.

39. H. Brezis and H.-M. Nguyen, The BBM formula revisited, Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 27 (2016), 515–533.  

38. H.-M. Nguyen and M. S. Vogelius, Approximate cloaking for the full wave equation via change of variables : The Drude-Lorentz model, J. Math. Pures Appl. 106 (2016), 797–836.

37. H.-M. Nguyen, Cloaking using complementary media in the quasistatic regime, Ann. Inst. H. Poincaré Anal. Non Linéaire, 33 (2016), 1509–1518.

36. H. Brezis and H.-M. Nguyen, Two subtle convex nonlocal approximations of the BV- norm, Nonlinear Anal. 137 (2016), 222–245. 

35. H.-M. Nguyen, Limiting absorption principle and well-posedness for the Helmholtz equa- tion with sign changing coefficients, J. Math. Pures Appl. 106 (2016), 342–374.

34. H.-M. Nguyen and H. L. Nguyen, Cloaking using complementary media for the Helmholtz equation and a three spheres inequality for second order elliptic equations, Trans. Amer. Math. Soc. B 2 (2015), 93-112.

33. H.-M. Nguyen and V. L. Nguyen, Generalized Impedance Boundary Conditions for Stron- gly Absorbing Obstacles : Time Dependent Wave Equations, Math. Models Appl. Sci. 25 (2015), 1927-1960.

32. J.-M. Coron and H.-M. Nguyen, Dissipative boundary conditions for nonlinear hyperbolic equations : sharp conditions through an approach via time delay equations, SIAM J. Math. Anal. 47 (2015), 2220–2240.

31. H.-M. Nguyen, Cloaking via anomalous localized resonance for doubly complementary media in the quasi static regime, J. Eur. Math. Soc. (JEMS) 17 (2015), 1327–1365.

30. H.-M. Nguyen, Cloaking via anomalous localized resonance. A connection between the localized resonance and the blow up of the power for doubly complementary media, C. R. Math. Acad. Sci. Paris 353 (2015), 41–46.

29. H.-M. Nguyen and H. L. Nguyen, Localized and complete resonance in plasmonic struc- tures, ESAIM Math. Model. Numer. Anal. 49 (2015), 741–754.

28. H.-M. Nguyen, Superlensing using complementary media, Ann. Inst. H. Poincaré Anal. Non Linéaire 32 (2015), 471–484. 

27. H.-M. Nguyen, Asymptotic behavior of solutions to the Helmholtz equations with sign changing coefficients, Trans. Amer. Math. Soc. 367 (2015), 6581–6595

26. H.-M. Nguyen, Estimates for the topological degree and related topics, Journal of Fixed Point Theory and Applications 15 (2014), 185-215.

25. J. Lin, S. H. Oh, H.-M. Nguyen, and F. Reitich, Field enhancement and saturation of millimeter waves inside a metallic nanogap, Optics Express 22 (2014), 14402–14410.

24. H.-M. Nguyen, On a regularized scheme for approximate acoustic cloaking using trans- formation optics, SIAM J. Math. Anal. 45 (2013), 3034–3049.

23. J. Brandman, R. V. Kohn, and H.-M. Nguyen, Energy-driven formation of conical singularities in constrained thin sheets, J. Elasticity 113 (2013), 251–264.

22. R. V. Kohn and H.-M. Nguyen, Analysis of a compressed thin film bonded to a compliant substrate : the energy scaling law, J. Nonlinear Sci. 23 (2013), 343–362. 

21. H.-M. Nguyen and M. S. Vogelius, Approximate cloaking for the full wave equation, SIAM J. Math. Anal., 44 (2012), 1894-1924.

20. H.-M. Nguyen and M. S. Vogelius, Full Range Scattering Estimates and their Application to Cloaking.Arch. Ration. Mech. Anal. 203 (2012), 769-807.

19. H.-M. Nguyen, Approximate cloaking for the Helmholtz equation via transformation optics and consequences for perfect cloaking, 65 (2012), 155–186.

18. H.-M. Nguyen, Some inequalities related to Sobolev norms, Calc. Var. Partial Differential Equations, 41 (2011), 483–509.

17. H. Brezis and H.-M. Nguyen, The Jacobian determinant revisisted, Invent. Math. 185 (2011), 17–54.

16. H.-M. Nguyen, Γ-convergence, Sobolev norms, and BV functions, Duke Math. J., 157 (2011), 495–533.

15. H. Brezis and H.-M. Nguyen, On a new class of functions related to VMO, C. R. Math. Acad. Sci. Paris 349 (2011), 157–160.  

14. H. Brezis and H.-M. Nguyen, On the distributional Jacobian of maps from SN into SN in fractional Sobolev and Hölder spaces, Ann. of Math. 173 (2011), 1141-1183.

13. H.-M. Nguyen, Cloaking for the Helmholtz equation via change of variables in the whole spaces, Comm. Pure Appl. Math. 63 (2010), 1505–1524.

12. H.-M. Nguyen and L. A. Peletier, Monotonicity of the peak time in turnover models, C. R. Math. Acad. Sci. Paris 347 (2009), 495–500.

11. H.-M. Nguyen and M. S. Vogelius, A representation formula for the voltage perturbations caused by diametrically small conductivity inhomogeneities. Proof of uniform validity, Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009), 2283–2315.

10. H.-M. Nguyen and L. A. Peletier, Monotonicity of Time to Peak Response with respect to Drug Dose for Turnover Models, Differential and Integral Equations 22 (2009), 1–26.

9. H.-M. Nguyen Inequalities related to liftings and applications, C. R. Math. Acad. Sci. Paris 346 (2008), 957–962.

8. H. Haddar, P. Joly, and H.-M. Nguyen, Generalized impedance boundary conditions for scattering by strongly absorbing obstacles : The case of Maxwell’s equation, Math. Mod. Meth. Appl. Sci., 18 (2008), 1787–1827.

7. H.-M. Nguyen, Further characterizations of Sobolev spaces, J. European Math. Soc., 10 (2008), 191–229.

6. H.-M. Nguyen, Γ-convergence and Sobolev norms, C. R. Acad. Sci. Paris 345 (2007), 679–684.

5. H.-M. Nguyen, Optimal constant in a new estimate for the degree, J. d’Analyse Math., 101 (2007), 367–395.

4. J. Bourgain and H.-M. Nguyen, A new characterization of Sobolev spaces, C. R. Acad. Sci. Paris, 343 (2006), 75–80.

3. H.-M. Nguyen, Some new characterizations of Sobolev spaces, J. Funct. Anal., 237 (2006), 689–720.

2. J. Bourgain, H. Brezis, and H.-M. Nguyen, A new estimate for the topological degree, C. R. Acad. Sci. Paris, 340 (2005), 787–791. 

1. H. Haddar, P. Joly, and H.-M. Nguyen, Generalized impedance boundary conditions for scattering by strongly absorbing obstacles : The scalar case, Math. Mod. Meth. Appl. Sci., 15 (2005), 1273–1300.

Proceeding

C1. J.-M. Coron and H.-M. Nguyen, Null-controllability, exact controllability, and stabiliza- tion of hyperbolic systems for the optimal time, 59th IEEE Conference on Decision and Control (CDC), Jeju Island, Republic of Korea, December 14-18, 2020.

Unpublished work

N1. H.-M. Nguyen and D. Spirn, Recovering a potential from Cauchy data via complex geome- trical optics solutions, http ://arxiv.org/pdf/1403.2255.pdf.