Bibliography

Publications of the year

Articles in International Peer-Reviewed Journals

• 1N. Ayi, E. Faou.
  Analysis of an asymptotic preserving scheme for stochastic linear kinetic equations in the diffusion limit, in: SIAM/ASA Journal on Uncertainty Quantification, 2019, vol. 7, n^o 2, pp. 760-785, https://arxiv.org/abs/1803.06130. [ DOI : 10.1137/18M1175641 ]
  https://hal.archives-ouvertes.fr/hal-01734515
• 2I. Bailleul, A. Debussche, M. Hofmanova.
  Quasilinear generalized parabolic Anderson model, in: Stochastics and Partial Differential Equations: Analysis and Computations, 2019, vol. 7, n^o 1, pp. 40-63, https://arxiv.org/abs/1610.06726. [ DOI : 10.1007/s40072-018-0121-1 ]
  https://hal.archives-ouvertes.fr/hal-01389489
• 3K. Belabas, D. Bernardi, B. Perrin-Riou.
  Polygones fondamentaux d'une courbe modulaire, in: Publications Mathématiques de Besançon : Algèbre et Théorie des Nombres, 2019, pp. 1-37, forthcoming.
  https://hal.archives-ouvertes.fr/hal-01828430
• 4J. Bernier.
  Bounds on the growth of high discrete Sobolev norms for the cubic discrete nonlinear Schrödinger equations on $h\mathbb{Z}$, in: Discrete and Continuous Dynamical Systems - Series A, 2019, vol. 39, n^o 6, pp. 3179-3195, https://arxiv.org/abs/1805.02468. [ DOI : 10.3934/dcds.2019131 ]
  https://hal.archives-ouvertes.fr/hal-01785953
• 5J. Bernier.
  Optimality and resonances in a class of compact finite difference schemes of high order, in: Calcolo, 2019, vol. 56, n^o 2, article 12 https://arxiv.org/abs/1710.02953, forthcoming. [ DOI : 10.1007/s10092-019-0309-4 ]
  https://hal.archives-ouvertes.fr/hal-01612326
• 6J. Bernier, E. Faou.
  Existence and stability of traveling waves for discrete nonlinear Schroedinger equations over long times, in: SIAM Journal on Mathematical Analysis, 2019, vol. 51, n^o 3, pp. 1607–1656, https://arxiv.org/abs/1805.03578. [ DOI : 10.1137/18M1186484 ]
  https://hal.archives-ouvertes.fr/hal-01788398
• 7J. Bernier, M. Mehrenberger.
  Long-time behavior of second order linearized Vlasov-Poisson equations near a homogeneous equilibrium, in: Kinetic and Related Models , 2020, vol. 13, n^o 1, pp. 129-168, https://arxiv.org/abs/1903.08374. [ DOI : 10.3934/krm.2020005 ]
  https://hal.archives-ouvertes.fr/hal-02070138
• 8F. Casas, P. Chartier, A. Murua.
  Continuous changes of variables and the Magnus expansion, in: Journal of Physics Communications, 2019, pp. 1-14, forthcoming. [ DOI : 10.1088/2399-6528/ab42c1 ]
  https://hal.inria.fr/hal-02393566
• 9S. Cerrai, A. Debussche.
  Large deviations for the two-dimensional stochastic Navier-Stokes equation with vanishing noise correlation, in: Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2019, vol. 55, n^o 1, pp. 211-236, https://arxiv.org/abs/1603.02527 . [ DOI : 10.1214/17-AIHP881 ]
  https://hal.archives-ouvertes.fr/hal-01942681
• 10P. Chartier, N. Crouseilles, M. Lemou, F. Méhats, X. Zhao.
  Uniformly accurate methods for Vlasov equations with non-homogeneous strong magnetic field, in: Mathematics of Computation, 2019, vol. 88, n^o 320, pp. 2697-2736. [ DOI : 10.1090/mcom/3436 ]
  https://hal.inria.fr/hal-01703477
• 11P. Chartier, L. Le Treust, F. Méhats.
  Uniformly accurate time-splitting methods for the semiclassical linear Schrödinger equation, in: ESAIM: Mathematical Modelling and Numerical Analysis, 2019, vol. 53, n^o 2, pp. 443-473, https://arxiv.org/abs/1601.04825. [ DOI : 10.1051/m2an/2018060 ]
  https://hal.archives-ouvertes.fr/hal-01257753
• 12P. Chartier, M. Lemou, F. Méhats, G. Vilmart.
  A new class of uniformly accurate numerical schemes for highly oscillatory evolution equations, in: Foundations of Computational Mathematics, 2019, pp. 1-29, forthcoming. [ DOI : 10.1007/s10208-019-09413-3 ]
  https://hal.archives-ouvertes.fr/hal-01666472
• 13P. Chartier, M. Lemou, F. Méhats, G. Vilmart.
  Highly-oscillatory problems with time-dependent vanishing frequency, in: SIAM Journal on Numerical Analysis, 2019, vol. 57, n^o 2, pp. 925–944, https://arxiv.org/abs/1807.07835. [ DOI : 10.1137/18M1203456 ]
  https://hal.inria.fr/hal-01845614
• 14A. Crestetto, N. Crouseilles, G. Dimarco, M. Lemou.
  Asymptotically complexity diminishing schemes (ACDS) for kinetic equations in the diffusive scaling, in: Journal of Computational Physics, 2019, vol. 394, pp. 243-262. [ DOI : 10.1016/j.jcp.2019.05.032 ]
  https://hal.archives-ouvertes.fr/hal-01849671
• 15A. Debussche, J. Martin.
  Solution to the stochastic Schrödinger equation on the full space, in: Nonlinearity, 2019, vol. 32, n^o 4, pp. 1147-1174, https://arxiv.org/abs/1707.06431. [ DOI : 10.1088/1361-6544/aaf50e ]
  https://hal.archives-ouvertes.fr/hal-01579115
• 16M. Fontaine, M. Lemou, F. Méhats.
  Stable Ground States for the HMF Poisson Model, in: Annales de l'Institut Henri Poincaré (C) Non Linear Analysis, 2019, vol. 36, n^o 1, pp. 217-255, https://arxiv.org/abs/1709.02234. [ DOI : 10.1016/j.anihpc.2018.05.002 ]
  https://hal.archives-ouvertes.fr/hal-01582008
• 17M. Lemou, A. M. M. Luz, F. Méhats.
  Nonlinear instability of inhomogeneous steady states solutions to the HMF Model, in: Journal of Statistical Physics, 2019, https://arxiv.org/abs/1902.09785, forthcoming. [ DOI : 10.1007/s10955-019-02448-4 ]
  https://hal.archives-ouvertes.fr/hal-02048776
• 18Y. Li, N. Crouseilles, Y. Sun.
  Numerical simulations of Vlasov-Maxwell equations for laser plasmas based on Poisson structure, in: Journal of Computational Physics, 2020, pp. 1-34.
  https://hal.inria.fr/hal-02391668

Conferences without Proceedings

• 19A. Muller-Gueudin, A. Debussche, A. Crudu.
  Modeling of gene regulation networks by deterministic processes by pieces, in: Journée de la Fédération Charles Hermite, Vandoeuvre-les-Nancy, France, June 2019, pp. 1-37.
  https://hal.archives-ouvertes.fr/hal-02360992

Other Publications

• 20P. Alphonse, J. Bernier.
  Polar decomposition of semigroups generated by non-selfadjoint quadratic differential operators and regularizing effects, January 2020, https://arxiv.org/abs/1909.03662 - working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-02280971
• 21M. Antoñana, P. Chartier, J. Makazaga, A. Murua.
  Global time-regularization of the gravitational N -body problem, January 2020, working paper or preprint.
  https://hal.inria.fr/hal-02431607
• 22J. Bernier, F. Casas, N. Crouseilles.
  Splitting methods for rotations: application to vlasov equations, July 2019, working paper or preprint.
  https://hal.inria.fr/hal-02178952
• 23J. Bernier, N. Crouseilles, Y. Li.
  Exact splitting methods for kinetic and Schrödinger equations, December 2019, https://arxiv.org/abs/1912.13221 - working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-02425605
• 24J. Bernier, E. Faou, B. Grebert.
  Long time behavior of the solutions of NLW on the d-dimensional torus, September 2019, https://arxiv.org/abs/1906.05107 - working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-02151338
• 25M. Briant, A. Debussche, J. Vovelle.
  The Boltzmann equation with an external force on the torus: Incompressible Navier-Stokes-Fourier hydrodynamical limit, June 2019, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-02150286
• 26C. Buet, B. Després, G. Morel.
  TDG method for Friedrichs systems and the P N model in 2D, November 2019, working paper or preprint.
  https://hal.sorbonne-universite.fr/hal-02372279
• 27P. Chartier, N. Crouseilles, M. Lemou, F. Méhats, X. Zhao.
  Uniformly accurate methods for three dimensional Vlasov equations under strong magnetic field with varying direction, July 2019, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-02179534
• 28A. Crestetto, N. Crouseilles, G. Dimarco, M. Lemou.
  A new deviational Asymptotic Preserving Monte Carlo method for the homogeneous Boltzmann equation, December 2019, working paper or preprint.
  https://hal.inria.fr/hal-02413232
• 29N. Crouseilles, L. Einkemmer, J. Massot.
  Exponential methods for solving hyperbolic problems with application to kinetic equations, October 2019, https://arxiv.org/abs/1910.12720 - working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-02321916
• 30G. Da Prato, A. Debussche.
  Estimate for P t D for the stochastic Burgers equation, November 2019, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-02347398
• 31G. Da Prato, A. Debussche.
  Gradient Estimates and Maximal Dissipativity for the Kolmogorov Operator in ${\Phi }_2^4$, December 2019, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-02390677
• 32A. Rosello.
  Weak and strong mean-field limits for stochastic Cucker-Smale particle systems, June 2019, https://arxiv.org/abs/1905.02499 - working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-02120106

References in notes

• 33C. Birdsall, A. Langdon.
  Plasmas physics via computer simulations, Taylor and Francis, New York, 2005.
• 34A. Brizard, T. Hahm.
  Foundations of nonlinear gyrokinetic theory, in: Reviews of Modern Physics, 2007, vol. 79.
• 35J. Carr.
  Applications of Centre Manifold Theory, in: Applied Mathematical Sciences Series, 1981, vol. 35.
• 36P. Chartier, N. Crouseilles, M. Lemou, F. Méhats.
  Uniformly accurate numerical schemes for highly-oscillatory Klein-Gordon and nonlinear Schrödinger equations, in: Numer. Math., 2015, vol. 129, pp. 513–536.
• 37P. Chartier, A. Murua, J. Sanz-Serna.
  Higher-order averaging, formal series and numerical integration III: error bounds, in: Foundation of Comput. Math., 2015, vol. 15, pp. 591–612.
• 38A. Debussche, J. Vovelle.
  Diffusion limit for a stochastic kinetic problem, in: Commun. Pure Appl. Anal., 2012, vol. 11, pp. 2305–2326.
• 39E. Faou, F. Rousset.
  Landau damping in Sobolev spaces for the Vlasov-HMF model, in: Arch. Ration. Mech. Anal., 2016, vol. 219, pp. 887–902.
• 40E. Hairer, C. Lubich, G. Wanner.
  Geometric Numerical Integration. Structure-Preserving Algorithms for Ordinary Differential Equations, Second edition, Springer Series in Computational Mathematics 31, Springer, Berlin, 2006.
• 41S. Jin, H. Lu.
  An Asymptotic-Preserving stochastic Galerkin method for the radiative heat transfer equations with random inputs and diffusive scalings, in: J. Comp. Phys., 2017, vol. 334, pp. 182–206.
• 42M. Lemou, F. Méhats, P. Raphaël.
  Orbital stability of spherical galactic models, in: Invent. Math., 2012, vol. 187, pp. 145–194.
• 43C. Mouhot, C. Villani.
  On Landau damping, in: Acta Math., 2011, vol. 207, pp. 29–201.
• 44S. Nazarenko.
  Wave turbulence, Springer-Verlag, 2011.
• 45L. Perko.
  Higher order averaging and related methods for perturbed periodic and quasi-periodic systems, in: SIAM J. Appl. Math., 1969, vol. 17, pp. 698–724.