Papers

• Absorbing boundary conditions for reaction diffusion equation.
  IMA J. Appl. Math. 68 (2), 167-184.


• Réflexion des singularités pour Schrödinger.
  Comm. Partial Differential Equations 29 (5-6), 707-761, 2004.


• Long time existence for small data nonlinear Klein-Gordon equations on tori and spheres (with J. M. Delort).
  Int. Math. Res. Not. 37, 1897-1966, 2004.


• Design of absorbing boundary conditions for Schrödinger equations in R^d.
  SIAM J. Numer. Anal. 42 (4), 1527-1551, 2004


• Propagation et réflexion des singularités pour l'équation de Schrödinger non linéaire
  Ann. Inst. Fourier (Grenoble) 55 (2), 573-671, 2005.


• Microlocal smoothing effect for the nonlinear Schrödinger equation.
  SIAM J. Math. Anal. 37 (2), 549-597, 2005.


• A nonlinear approach to absorbing boundary conditions for the semilinear wave equation.
  Math. Comp.75, 565-594, 2006.


• Absorbing boundary conditions for nonlinear scalar partial differential equations
  Comput. Methods Appl. Mech. Engrg. 195, 3760-3775, 2006.


• Absorbing boundary conditions for nonlinear Schrödinger equations
  Numerische Mathematik 104, 103-127, 2006.


• Long-time existence for semi-linear Klein-Gordon equations with small Cauchy data on Zoll manifolds (with J. M. Delort)
  Amer. J. Math. 128, 1187-1218, 2006.


• Bounded almost global solutions for non hamiltonian semi-linear Klein-Gordon equations with radial data on compact revolution hypersurfaces (with J. M. Delort)
  Ann. Inst. Fourier (Grenoble) 56, 1419-1456, 2006.


• Almost global existence for Hamiltonian semi-linear Klein-Gordon equations with small Cauchy data on Zoll manifolds (with D. Bambusi, J. M. Delort and B. Grébert)
  Comm. Pure. Appl. Math. 60, 1665-1690, 2007.


• Nonlinear Nonoverlapping Schwarz Waveform Relaxation for Semilinear Wave Propagation (with L. Halpern)
  Math. Comp. 78, 865-889, 2009.


• Towards accurate artificial boundary conditions for nonlinear PDEs through examples (with X. Antoine and C. Besse)
  Cubo, 11 (4), 29-48, 2009.


• Standing ring blow up solutions to the N-dimensional quintic nonlinear Schrödinger equation (with P. Raphael)
  Comm. Math. Phys. 290 (3), 973-996, 2009.


• Schwarz waveform relaxation algorithms for semilinear reaction-diffusion equations (with F. Caetano, M. Gander and L. Halpern)
  Netw. Heterog. Media 5 (3), 487-505, 2010.


• Stable self similar blow up dynamics for slightly L² supercritical NLS equations (with F. Merle and P. Raphael)
  Geom. Funct. Anal. 20 (4), 1028-1071, 2010.


• Optimized and Quasi-Optimal Schwarz Waveform Relaxation for the One Dimensional Schrödinger equation (with L. Halpern)
  Math. Models Methods Appl. Sci. 20 (12). 2167-2199, 2010.


• Existence and uniqueness of minimal blow up solutions to an inhomogeneous mass critical NLS (with P. Raphael)
  J. Amer. Math. Soc. 24, 471-546, 2011.


• On the instability of the pseudoconformal blow up for the L² critical NLS (with F. Merle and P. Raphael)
  Accepted for publication in Amer. J. Math.


• Optimized Schwarz waveform relaxation and discontinuous Galerkin time stepping for heterogeneous problems (with C. Japhet and L. Halpern)
  Submitted.


• On collapsing ring blow up solutions to the mass supercritical NLS (with F. Merle and P. Raphael)
  Submitted.


• The Bounded L² Curvature Conjecture (with S. Klainerman and I. Rodnianski)
  Preprint.


• Parametrix for wave equations on a rough background I: regularity of the phase at initial time
  Preprint.


• Parametrix for wave equations on a rough background II: construction and control at initial time
  Preprint.


• Parametrix for wave equations on a rough background III: space-time regularity of the phase
  Preprint.


• Parametrix for wave equations on a rough background IV: control of the error term
  Preprint.