Miguel Rodrigues

Contact C.V. (vitæ) Enseignement Recherche (research)
Habilitation Présentation (Pré)publications Thèse

Mémoires

  1. « Asymptotic stability and modulation of periodic wavetrains. General theory & applications to thin film flows », L.M. Rodrigues,
    Habilitation à diriger des recherches, Lyon I (2013) : pdf.
  2. « Comportement en temps long des fluides visqueux bidimensionnels », L.M. Rodrigues,
    Thèse de doctorat, Grenoble I (2007) : ps, pdf.

Articles

  1. "Small-amplitude finite-depth Stokes waves are transversally unstable", Z. Jiao, L.M. Rodrigues, C. Sun & Z. Yang,
    soumis, 29 p. : pdf.
  2. "Phase sinks and sources around two-dimensional periodic-wave solutions of reaction-diffusion-advection systems", B. Melinand & L.M. Rodrigues,
    soumis, 69 p. : pdf.
  3. « Convective stability in scalar balance laws », L. Garénaux & L.M. Rodrigues,
    Differential and Integral Equations, Vol. 38 (2025), no. 1-2, p. 71-110 : pdf.
  4. « Existence and stability of nonmonotone hydraulic shocks for the Saint Venant equations of inclined thin-film flow », G. Faye, L.M. Rodrigues, Z. Yang & K. Zumbrun,
    Archive for Rational Mechanics and Analysis, Vol. 248 (2024), no. 5, article no. 82, 49p.: pdf.
  5. « Linear asymptotic stability of small-amplitude periodic waves of the generalized Korteweg-de Vries equations », C. Audiard, L.M. Rodrigues & C. Sun,
    Proceedings of the American Mathematical Society, Vol. 152 (2024), no. 7, p. 2905-2921 : pdf.
  6. « Spectral instability of small-amplitude periodic waves of the electronic Euler-Poisson system », P. Noble, L.M. Rodrigues & C. Sun,
    Nonlinearity, Vol. 36 (2023), no. 9, p. 4615-4640 : pdf.
  7. « Convective-wave solutions to the Richard-Gavrilyuk model for inclined shallow water flow », L.M. Rodrigues, Z. Yang & K. Zumbrun,
    Water Waves, Vol. 5 (2023), no. 1, p. 1-39 : pdf.
  8. « Asymptotically preserving particle methods for strongly magnetized plasmas in a torus », F. Filbet & L.M. Rodrigues,
    Journal of Computational Physics, Vol. 480 (2023), Paper no. 112015, 23 p. : pdf.
  9. « Exponential asymptotic stability of Riemann shocks of hyperbolic systems of balance laws », G. Faye & L.M. Rodrigues,
    SIAM Journal on Mathematical Analysis, Vol. 55 (2023), no. 6, p. 6425-6456 : pdf.
  10. « Uniform asymptotic stability for convection-reaction-diffusion equations in the inviscid limit towards Riemann shocks », P. Blochas & L.M. Rodrigues,
    Annales de l'I.H.P. (C) - Analyse non linéaire, Vol. 41 (2024), no. 3, p. 615-661: pdf.
  11. « About plane periodic waves of the nonlinear Schrödinger equations », C. Audiard & L.M. Rodrigues,
    Bulletin de la Société Mathématique de France, Vol. 150 (2022), no. 1, p. 111-207 : pdf.
  12. « Stability and instability in scalar balance laws: fronts and periodic waves », V. Duchêne & L.M. Rodrigues,
    Analysis & PDE, Vol. 15 (2022), no. 7, p. 1807-1859 : pdf.
  13. « Convergence analysis of asymptotic preserving schemes for strongly magnetized plasmas », F. Filbet, L.M. Rodrigues & H. Zakerzadeh,
    Numerische Mathematik, Vol. 149 (2021), no. 3, p. 549-593 : pdf.
  14. « Modulated equations of Hamiltonian PDEs and dispersive shocks », S. Benzoni-Gavage, C. Mietka & L.M. Rodrigues,
    Nonlinearity, Vol. 34 (2021), no. 1, p. 578-641 : pdf.
  15. « Asymptotics of the three dimensional Vlasov equation in the large magnetic field limit », F. Filbet & L.M. Rodrigues,
    Journal de l'École Polytechnique - Mathématiques, Vol. 7 (2020), p. 1009-1067 : pdf.
  16. « Large-time asymptotic stability of Riemann shocks of scalar balance laws », V. Duchêne & L.M. Rodrigues,
    SIAM Journal on Mathematical Analysis, Vol. 52 (2020), no. 1, p. 792-820 : pdf.
  17. « Spectral stability of inviscid roll waves», M.A. Johnson, P. Noble, L.M. Rodrigues, Z. Yang & K. Zumbrun,
    Communications in Mathematical Physics, Vol. 367 (2019), no. 1, p. 265-316 : pdf.
  18. « Stability of periodic waves in Hamiltonian PDEs of either long wavelength or small amplitude », S. Benzoni-Gavage, C. Mietka & L.M. Rodrigues,
    Indiana University Mathematics Journal, Vol. 69 (2020), no. 2, p. 545-619 : pdf.
  19. « Large-time behavior of solutions to Vlasov-Poisson-Fokker-Planck equations: from evanescent collisions to diffusive limit », M. Herda & L.M. Rodrigues,
    Journal of Statistical Physics , Vol. 170 (2018), no. 5, p. 895-931 : pdf.
  20. « Linear asymptotic stability and modulation behavior near periodic waves of the Korteweg-de Vries equation », L.M. Rodrigues,
    Journal of Functional Analysis, Vol. 274 (2018), no. 9, p. 2553-2605 : pdf.
  21. « Asymptotically preserving particle-in-cell methods for inhomogeneous strongly magnetized plasmas », F. Filbet & L.M. Rodrigues,
    SIAM Journal on Numerical Analysis, Vol. 55 (2017), no. 5, p. 2416-2443 : pdf.
  22. « Anisotropic Boltzmann-Gibbs Dynamics of Strongly Magnetized Vlasov-Fokker-Planck Equations », M. Herda & L.M. Rodrigues,
    Kinetic and Related Models , Vol. 12 (2019), no. 3, p. 593-636 : pdf.
  23. « Asymptotically stable particle-in-cell methods for the Vlasov-Poisson system with a strong external magnetic field », F. Filbet & L.M. Rodrigues,
    SIAM Journal on Numerical Analysis, Vol. 54 (2016), no. 2, p. 1120-1146 : pdf.
  24. « Co-periodic stability of periodic waves in some Hamiltonian PDEs », S. Benzoni-Gavage, C. Mietka & L.M. Rodrigues,
    Nonlinearity, Vol. 29 (2016), no. 11, p. 3241-3308 : pdf.
  25. « Spectral validation of the Whitham equations for periodic waves of lattice dynamical systems », B. Kabil & L.M. Rodrigues,
    Journal of Differential Equations, Vol. 260 (2016), no. 3, p. 2994-3028 : pdf.
  26. « Periodic-coefficient damping estimates, and stability of large-amplitude roll waves in inclined thin film flow », L.M. Rodrigues & K. Zumbrun,
    SIAM Journal on Mathematical Analysis, Vol. 48 (2016), no. 1, p. 268-280 : pdf.
  27. « Invariant measures for a stochastic Fokker-Planck equation », S. de Moor, L.M. Rodrigues & J. Vovelle,
    Kinetic and Related Models , Vol. 11 (2018), no. 2, p. 357-395 : pdf.
  28. « Stability of viscous St. Venant roll-waves: from onset to infinite-Froude number limit », B. Barker, M.A. Johnson, P. Noble, L.M. Rodrigues & K. Zumbrun,
    Journal of Nonlinear Science, Vol. 27 (2017), no. 1, p. 285-342 : pdf.
  29. « Slow modulations of periodic waves in Hamiltonian PDEs, with application to capillary fluids », S. Benzoni-Gavage, P. Noble & L.M. Rodrigues,
    Journal of Nonlinear Science, Vol. 24 (2014), no. 4, p. 711-768 : pdf.
  30. « Behavior of periodic solutions of viscous conservation laws under localized and nonlocalized perturbations », M.A. Johnson, P. Noble, L.M. Rodrigues & K. Zumbrun,
    Inventiones mathematicae, Vol. 197 (2014), no. 1, p. 115-213 : pdf.
  31. « Nonlinear modulational stability of periodic traveling-wave solutions of the generalized Kuramoto-Sivashinsky equation », B. Barker, M.A. Johnson, P. Noble, L.M. Rodrigues & K. Zumbrun,
    Physica D: Nonlinear Phenomena, Vol. 258 (2013), p. 11-46 : pdf.
  32. « Spectral stability of periodic wave trains of the Korteweg-de Vries/Kuramoto-Sivashinsky equation in the Korteweg-de Vries limit », M.A. Johnson, P. Noble, L.M. Rodrigues & K. Zumbrun,
    Transactions of the American Mathematical Society, Vol. 367 (2015), no. 3, p. 2159-2212 : pdf.
  33. « Nonlocalized modulation of periodic reaction diffusion waves: the Whitham equation », M.A. Johnson, P. Noble, L.M. Rodrigues & K. Zumbrun,
    Archive for Rational Mechanics and Analysis, no. 2 (2013), p. 669-692 : pdf.
  34. « Nonlocalized modulation of periodic reaction diffusion waves: nonlinear stability », M.A. Johnson, P. Noble, L.M. Rodrigues & K. Zumbrun,
    Archive for Rational Mechanics and Analysis, no. 2 (2013), p. 693-715 : pdf.
  35. « Whitham's Modulation Equations and Stability of Periodic Wave Solutions of the Korteweg-de Vries-Kuramoto-Sivashinsky Equation », P. Noble & L.M. Rodrigues,
    Indiana University Mathematics Journal, Vol. 62 (2013), no. 3, p. 753-783 : pdf.
  36. « Metastability of solitary roll wave solutions of the St. Venant equations with viscosity », B. Barker, M.A. Johnson, L.M. Rodrigues & K. Zumbrun,
    Physica D: Nonlinear Phenomena, Vol. 240, no. 16 (2011), p. 1289-1310 : pdf.
  37. « Vortex-like finite-energy asymptotic profiles for isentropic compressible flows », L.M. Rodrigues,
    Indiana University Mathematics Journal, Vol. 58 (2009), no. 4, p. 1747-1776 : ps, pdf.
  38. « Asymptotic stability of Oseen vortices for a density-dependent incompressible viscous fluid », L.M. Rodrigues,
    Annales de l'I.H.P. (C) - Analyse non linéaire, Vol. 26, Issue 2 (2009), p. 625-648 : ps, pdf.
  39. « Sur le temps de vie de la turbulence bidimensionnelle », Th. Gallay & L.M. Rodrigues,
    Annales de la Faculté des Sciences de Toulouse, Sér. 6, Vol. 17, no. 4 (2008), p. 719-733 : ps, pdf.

Notes et comptes-rendus

  1. « Space-modulated stability and averaged dynamics », L.M. Rodrigues,
    Journées Équations aux Dérivées Partielles, Roscoff (2015), Exp. no. 8 : pdf.
  2. « Note on the stability of viscous roll-waves », B. Barker, M.A. Johnson, P. Noble, L.M. Rodrigues & K. Zumbrun,
    Comptes Rendus Mécanique, Vol. 345 (2017), no. 2, p. 125-129 : pdf.
  3. « Stability of periodic waves in Hamiltonian PDEs », S. Benzoni-Gavage, P. Noble & L.M. Rodrigues,
    Journées Équations aux Dérivées Partielles, Biarritz (2013), Exp. no. 2 : pdf.
  4. « Stability of periodic Kuramoto-Sivashinsky waves », B. Barker, M.A. Johnson, P. Noble, L.M. Rodrigues & K. Zumbrun,
    Applied Mathematics Letters , Vol. 25, Issue 5 (2012), p. 824-829 : pdf.
  5. « Whitham averaged equations and modulational stability of periodic traveling waves of a hyperbolic-parabolic balance law », B. Barker, M.A. Johnson, P. Noble, L.M. Rodrigues & K. Zumbrun,
    Journées Équations aux Dérivées Partielles, Port-d'Albret (2010), Exp. no. 3 : pdf.