Miguel Rodrigues

Contact C.V. (vitæ) Enseignement Recherche (research)

Memoirs

  1. "Asymptotic stability and modulation of periodic wavetrains. General theory & applications to thin film flows", L.M. Rodrigues,
    Habilitation, Lyon I (2013) : pdf.
  2. « Comportement en temps long des fluides visqueux bidimensionnels », L.M. Rodrigues,
    Ph.D., Grenoble I (2007) : ps, pdf.
    In French.

Papers

  1. "Small-amplitude finite-depth Stokes waves are transversally unstable", Z. Jiao, L.M. Rodrigues, C. Sun & Z. Yang,
    submitted, 29 p. : pdf.
  2. "Phase sinks and sources around two-dimensional periodic-wave solutions of reaction-diffusion-advection systems", B. Melinand & L.M. Rodrigues,
    submitted, 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, paper no. 82, 49 p.: 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.
    In French.

Notes & proceedings

  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.