Bibliography

Publications of the year

Doctoral Dissertations and Habilitation Theses

• 1R. Horsin.
  On long time behavior of certain Vlasov equations: Mathematics and Numerics, Université de Rennes 1, December 2017.
  https://tel.archives-ouvertes.fr/tel-01670352

Articles in International Peer-Reviewed Journals

• 2N. Arrizabalaga, L. Le Treust, N. Raymond.
  On the MIT Bag Model in the Non-relativistic Limit, in: Communications in Mathematical Physics, 2017, vol. 354, n^o 2, pp. 641-669. [ DOI : 10.1007/s00220-017-2916-8 ]
  https://hal.archives-ouvertes.fr/hal-01343717
• 3V. Banica, E. Faou, E. Miot.
  Collision of almost parallel vortex filaments, in: Communications on Pure and Applied Mathematics, 2017, vol. 70, n^o 2, pp. 378-405. [ DOI : 10.1002/cpa.21637 ]
  https://hal.archives-ouvertes.fr/hal-01170929
• 4W. Bao, L. Le Treust, F. Méhats.
  Dimension reduction for dipolar Bose-Einstein condensates in the strong interaction regime, in: Kinetic and Related Models , September 2017, vol. 10, n^o 3, pp. 553-571, https://arxiv.org/abs/1501.02177. [ DOI : 10.3934/krm.2017022 ]
  https://hal.archives-ouvertes.fr/hal-01101793
• 5F. Casas, N. Crouseilles, E. Faou, M. Mehrenberger.
  High-order Hamiltonian splitting for Vlasov-Poisson equations, in: Numerische Mathematik, 2017, vol. 135, n^o 3, pp. 769-801, https://arxiv.org/abs/1510.01841. [ DOI : 10.1007/s00211-016-0816-z ]
  https://hal.inria.fr/hal-01206164
• 6F. Castella, P. Chartier, J. Sauzeau.
  A formal series approach to the center manifold theorem, in: Foundations of Computational Mathematics, 2017, forthcoming. [ DOI : 10.1007/s10208-017-9371-y ]
  https://hal.inria.fr/hal-01279715
• 7P. Chartier, M. Lemou, F. Méhats.
  Highly-oscillatory evolution equations with multiple frequencies: averaging and numerics, in: Numerische Mathematik, December 2017, vol. 136, n^o 4, pp. 907-939. [ DOI : 10.1007/s00211-016-0864-4 ]
  https://hal.inria.fr/hal-01281950
• 8P. Chartier, F. Méhats, M. Thalhammer, Y. Zhang.
  Convergence of multi-revolution composition time-splitting methods for highly oscillatory differential equations of Schrödinger type, in: ESAIM: Mathematical Modelling and Numerical Analysis, September 2017, vol. 51, n^o 5, pp. 1859 - 1882. [ DOI : 10.1051/m2an/2017010 ]
  https://hal.archives-ouvertes.fr/hal-01636323
• 9M. Chaussade-Beaudouin, M. Dauge, E. Faou, Z. Yosibash.
  Free Vibrations of Axisymmetric Shells: Parabolic and Elliptic cases, in: Asymptotic Analysis, 2017, vol. 104, n^o 2, pp. 1-47, https://arxiv.org/abs/1602.00850. [ DOI : 10.3233/ASY-171426 ]
  https://hal.archives-ouvertes.fr/hal-01264125
• 10N. Crouseilles, G. Dimarco, M. Lemou.
  Asymptotic preserving and time diminishing schemes for rarefied gas dynamic, in: Kinetic and Related Models , 2017, vol. 10, pp. 643-668.
  https://hal.inria.fr/hal-01392412
• 11N. Crouseilles, S. A. Hirstoaga, X. Zhao.
  Multiscale Particle-in-Cell methods and comparisons for the long-time two-dimensional Vlasov-Poisson equation with strong magnetic field, in: Computer Physics Communications, October 2017, vol. 222, pp. 136-151.
  https://hal.archives-ouvertes.fr/hal-01496854
• 12N. Crouseilles, S. Jin, M. Lemou.
  Nonlinear Geometric Optics method based multi-scale numerical schemes for highly-oscillatory transport equations, in: Mathematical Models and Methods in Applied Sciences, 2017, vol. 27, n^o 11, pp. 2031-2070. [ DOI : 10.1142/S0218202517500385 ]
  https://hal.archives-ouvertes.fr/hal-01323721
• 13N. Crouseilles, M. Lemou, F. Méhats, X. Zhao.
  Uniformly accurate forward semi-Lagrangian methods for highly oscillatory Vlasov-Poisson equations, in: Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 2017, vol. 15, n^o 2, pp. 723-744. [ DOI : 10.1137/16M1059497 ]
  https://hal.inria.fr/hal-01286947
• 14G. Da Prato, A. Debussche.
  An integral inequality for the invariant measure of a stochastic reaction–diffusion equation, in: Journal of Evolution Equations, 2017, vol. 17, n^o 1, pp. 197-214, https://arxiv.org/abs/1511.07133. [ DOI : 10.1007/s00028-016-0349-z ]
  https://hal.archives-ouvertes.fr/hal-01235038
• 15S. Fournais, L. Le Treust, N. Raymond, J. Van Schaftingen.
  Semiclassical Sobolev constants for the electro-magnetic Robin Laplacian, in: Journal of the Mathematical Society of Japan, 2017, vol. 69, n^o 4, pp. 1667-1714, https://arxiv.org/abs/1603.02810. [ DOI : 10.2969/jmsj/06941667 ]
  https://hal.archives-ouvertes.fr/hal-01285311
• 16R. L. Frank, F. Méhats, C. Sparber.
  Averaging of nonlinear Schrödinger equations with strong magnetic confinement, in: Communications in Mathematical Sciences, 2017, vol. 15, n^o 7, pp. 1933-1945, https://arxiv.org/abs/1611.01574 - 12 pages. [ DOI : 10.4310/CMS.2017.v15.n7.a7 ]
  https://hal.archives-ouvertes.fr/hal-01397325
• 17M. Lemou, A. M. Luz, F. Méhats.
  Nonlinear stability criteria for the HMF Model, in: Archive for Rational Mechanics and Analysis, 2017, vol. 224, n^o 2, pp. 353-380, https://arxiv.org/abs/1509.08637. [ DOI : 10.1007/s00205-017-1077-4 ]
  https://hal.archives-ouvertes.fr/hal-01207626
• 18M. Lemou, F. Méhats, X. Zhao.
  Uniformly accurate numerical schemes for the nonlinear dirac equation in the nonrelativistic limit regime, in: Communications in Mathematical Sciences, 2017, vol. 15, n^o 4, pp. 1107-1128. [ DOI : 10.4310/CMS.2017.v15.n4.a9 ]
  https://hal.archives-ouvertes.fr/hal-01313976
• 19F. Méhats, O. Pinaud.
  The quantum Liouville-BGK equation and the moment problem, in: Journal of Differential Equations, 2017, vol. 263, n^o 7, pp. 3737-3787, https://arxiv.org/abs/1512.01504. [ DOI : 10.1016/j.jde.2017.05.004 ]
  https://hal.archives-ouvertes.fr/hal-01255137
• 20F. Méhats, N. Raymond.
  Strong confinement limit for the nonlinear Schrödinger equation constrained on a curve, in: Annales Henri Poincaré, 2017, vol. 18, n^o 1, pp. 281-306. [ DOI : 10.1007/s00023-016-0511-8 ]
  https://hal.archives-ouvertes.fr/hal-01090045
• 21T. Wang, X. Zhao, J. Jiang.
  Unconditional and optimal $H^2$-error estimates of two linear and conservative finite difference schemes for the Klein-Gordon-Schrödinger equation in high dimensions, in: Advances in Computational Mathematics, 2017. [ DOI : 10.1007/s10444-017-9557-5 ]
  https://hal.archives-ouvertes.fr/hal-01576947
• 22X. Zhao.
  A combination of multiscale time integrator and two-scale formulation for the nonlinear Schrödinger equation with wave operator, in: Journal of Computational and Applied Mathematics, 2017, vol. 326, pp. 320 - 336. [ DOI : 10.1016/j.cam.2017.06.006 ]
  https://hal.archives-ouvertes.fr/hal-01576629
• 23X. Zhao.
  Uniformly accurate multiscale time integrators for second order oscillatory differential equations with large initial data, in: BIT Numerical Mathematics, 2017, vol. 57, n^o 3, pp. 649 - 683. [ DOI : 10.1007/s10543-017-0646-0 ]
  https://hal.archives-ouvertes.fr/hal-01591333

Scientific Books (or Scientific Book chapters)

• 24M. Chaussade-Beaudouin, M. Dauge, E. Faou, Z. Yosibash.
  High frequency oscillations of first eigenmodes in axisymmetric shells as the thickness tends to zero, in: Operator Theory Advances and Application, Recent Trends in Operator Theory and Partial Differential Equations - The Roland Duduchava Anniversary Volume, Birkhäuser/Springer, 2017, vol. 258, pp. 89-110, https://arxiv.org/abs/1603.01459. [ DOI : 10.1007/978-3-319-47079-5_5 ]
  https://hal.archives-ouvertes.fr/hal-01278861

Other Publications

• 25J. Bernier.
  Optimality and resonances in a class of compact finite difference schemes of high order, October 2017, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-01612326
• 26C.-E. Bréhier, A. Debussche.
  Kolmogorov Equations and Weak Order Analysis for SPDES with Nonlinear Diffusion Coefficient, 2017, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-01481966
• 27S. Cerrai, A. Debussche.
  Large deviations for the dynamic ${\Phi }_d^{2n}$ model, May 2017, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-01518465
• 28P. Chartier, M. Lemou, F. Méhats, G. Vilmart.
  A new class of uniformly accurate numerical schemes for highly oscillatory evolution equations, December 2017, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-01666472
• 29A. Crestetto, N. Crouseilles, M. Lemou.
  A particle micro-macro decomposition based numerical scheme for collisional kinetic equations in the diffusion scaling, January 2017, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-01439288
• 30N. Crouseilles, L. Einkemmer, M. Prugger.
  An exponential integrator for the drift-kinetic model, 2017, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-01538450
• 31N. Crouseilles, S. Jin, M. Lemou, L. Liu.
  Nonlinear Geometric Optics Based Multiscale Stochastic Galerkin Methods for Highly Oscillatory Transport Equations with Random Inputs *, April 2017, working paper or preprint.
  https://hal.inria.fr/hal-01501825
• 32A. De Bouard, A. Debussche, R. Fukuizumi.
  Long time behavior of Gross-Pitaevskii equation at positive temperature, 2017, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-01579123
• 33A. Debussche, J. Martin.
  Solution to the stochastic Schrödinger equation on the full space, 2017, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-01579115
• 34A. Debussche, M. J. Nguepedja Nankep.
  A Law of Large Numbers in the Supremum Norm for a Multiscale Stochastic Spatial Gene Network, November 2017, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-01636039
• 35A. Debussche, J. Vovelle.
  Approximation - diffusion in stochastically forced kinetic equations, July 2017, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-01567138
• 36M. Fontaine, M. Lemou, F. Méhats.
  Stable Ground States for the HMF Poisson Model, September 2017, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-01582008

References in notes

• 37E. Hairer.
  Geometric integration of ordinary differential equations on manifolds, in: BIT, 2001, vol. 41, pp. 996–1007.
• 38E. 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.
• 39E. Hairer, G. Wanner.
  Solving Ordinary Differential Equations II. Stiff and Differential-Algebraic Problems, Springer Series in Computational Mathematics 14, 2, Springer-Verlag, Berlin, 1996.
• 40C. Lubich.
  A variational splitting integrator for quantum molecular dynamics, in: Appl. Numer. Math., 2004, vol. 48, pp. 355–368.
• 41C. Lubich.
  On variational approximations in quantum molecular dynamics, in: Mathematics of Computation, 2009.
• 42J. M. Sanz-Serna, M. P. Calvo.
  Numerical Hamiltonian Problems, Chapman & Hall, London, 1994.