Team, Visitors, External Collaborators
Overall Objectives
Research Program
Application Domains
New Software and Platforms
New Results
Bilateral Contracts and Grants with Industry
Partnerships and Cooperations
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Publications of the year

Articles in International Peer-Reviewed Journals

N. 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, no 2, pp. 760-785, [ DOI : 10.1137/18M1175641 ]
I. Bailleul, A. Debussche, M. Hofmanova.
Quasilinear generalized parabolic Anderson model, in: Stochastics and Partial Differential Equations: Analysis and Computations, 2019, vol. 7, no 1, pp. 40-63, [ DOI : 10.1007/s40072-018-0121-1 ]
K. 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.
J. Bernier.
Bounds on the growth of high discrete Sobolev norms for the cubic discrete nonlinear Schrödinger equations on h, in: Discrete and Continuous Dynamical Systems - Series A, 2019, vol. 39, no 6, pp. 3179-3195, [ DOI : 10.3934/dcds.2019131 ]
J. Bernier.
Optimality and resonances in a class of compact finite difference schemes of high order, in: Calcolo, 2019, vol. 56, no 2, article 12, forthcoming. [ DOI : 10.1007/s10092-019-0309-4 ]
J. 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, no 3, pp. 1607–1656, [ DOI : 10.1137/18M1186484 ]
J. 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, no 1, pp. 129-168, [ DOI : 10.3934/krm.2020005 ]
F. 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 ]
S. 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, no 1, pp. 211-236, . [ DOI : 10.1214/17-AIHP881 ]
P. 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, no 320, pp. 2697-2736. [ DOI : 10.1090/mcom/3436 ]
P. 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, no 2, pp. 443-473, [ DOI : 10.1051/m2an/2018060 ]
P. 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 ]
P. Chartier, M. Lemou, F. Méhats, G. Vilmart.
Highly-oscillatory problems with time-dependent vanishing frequency, in: SIAM Journal on Numerical Analysis, 2019, vol. 57, no 2, pp. 925–944, [ DOI : 10.1137/18M1203456 ]
A. 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/ ]
A. Debussche, J. Martin.
Solution to the stochastic Schrödinger equation on the full space, in: Nonlinearity, 2019, vol. 32, no 4, pp. 1147-1174, [ DOI : 10.1088/1361-6544/aaf50e ]
M. 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, no 1, pp. 217-255, [ DOI : 10.1016/j.anihpc.2018.05.002 ]
M. Lemou, A. M. M. Luz, F. Méhats.
Nonlinear instability of inhomogeneous steady states solutions to the HMF Model, in: Journal of Statistical Physics, 2019,, forthcoming. [ DOI : 10.1007/s10955-019-02448-4 ]
Y. 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.

Conferences without Proceedings

A. 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.

Other Publications

P. Alphonse, J. Bernier.
Polar decomposition of semigroups generated by non-selfadjoint quadratic differential operators and regularizing effects, January 2020, - working paper or preprint.
M. Antoñana, P. Chartier, J. Makazaga, A. Murua.
Global time-regularization of the gravitational N -body problem, January 2020, working paper or preprint.
J. Bernier, F. Casas, N. Crouseilles.
Splitting methods for rotations: application to vlasov equations, July 2019, working paper or preprint.
J. Bernier, N. Crouseilles, Y. Li.
Exact splitting methods for kinetic and Schrödinger equations, December 2019, - working paper or preprint.
J. Bernier, E. Faou, B. Grebert.
Long time behavior of the solutions of NLW on the d-dimensional torus, September 2019, - working paper or preprint.
M. 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.
C. Buet, B. Després, G. Morel.
TDG method for Friedrichs systems and the P N model in 2D, November 2019, working paper or preprint.
P. 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.
A. 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.
N. Crouseilles, L. Einkemmer, J. Massot.
Exponential methods for solving hyperbolic problems with application to kinetic equations, October 2019, - working paper or preprint.
G. Da Prato, A. Debussche.
Estimate for P t D for the stochastic Burgers equation, November 2019, working paper or preprint.
G. Da Prato, A. Debussche.
Gradient Estimates and Maximal Dissipativity for the Kolmogorov Operator in Φ24, December 2019, working paper or preprint.
A. Rosello.
Weak and strong mean-field limits for stochastic Cucker-Smale particle systems, June 2019, - working paper or preprint.
References in notes
C. Birdsall, A. Langdon.
Plasmas physics via computer simulations, Taylor and Francis, New York, 2005.
A. Brizard, T. Hahm.
Foundations of nonlinear gyrokinetic theory, in: Reviews of Modern Physics, 2007, vol. 79.
J. Carr.
Applications of Centre Manifold Theory, in: Applied Mathematical Sciences Series, 1981, vol. 35.
P. 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.
P. 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.
A. Debussche, J. Vovelle.
Diffusion limit for a stochastic kinetic problem, in: Commun. Pure Appl. Anal., 2012, vol. 11, pp. 2305–2326.
E. Faou, F. Rousset.
Landau damping in Sobolev spaces for the Vlasov-HMF model, in: Arch. Ration. Mech. Anal., 2016, vol. 219, pp. 887–902.
E. 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.
S. 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.
M. Lemou, F. Méhats, P. Raphaël.
Orbital stability of spherical galactic models, in: Invent. Math., 2012, vol. 187, pp. 145–194.
C. Mouhot, C. Villani.
On Landau damping, in: Acta Math., 2011, vol. 207, pp. 29–201.
S. Nazarenko.
Wave turbulence, Springer-Verlag, 2011.
L. 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.