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Benjamin Texier


Maître de conférences.                                                                                                                                                      

Université Paris-Diderot (Paris 7)
Institut de Mathématiques de Jussieu, UMR CNRS 7586

adresse postale:
boite 186 -- 4, place Jussieu 75252 Paris Cedex 05

adresse physique:
175 rue du Chevaleret, 75013 Paris.
7E19,  +33 1 52 27 92 93.

Ecole Normale Supérieure
Département de Mathématiques et applications
bureau 9 (espace Cartan)
45 rue d'Ulm, 75005 Paris.

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Cours M2 Equations aux dérivées partielles non linéaires.

mise à jour le 6 janvier 2012.

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TD EDP (ENS, deuxième année, cours de Nicolas Burq).

mise à jour le 19 janvier 2012.

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Séminaire Analyse non-linéaire et EDP.

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Research interests:

•  Well-posedness and stability issues for the nonlinear Cauchy problem (with Toan Nguyen and Nicolas Lerner).


•  Weak turbulence (with Isabelle Gallagher and Laure Saint-Raymond).


•  Existence, stability and bifurcation issues for traveling waves (with Kevin Zumbrun).


• Anomalous diffusion; formal series expansions in hyperbolic and kinetic systems (with Antoine Mellet).


•  Highly-oscillating solutions of quasi-linear hyperbolic systems.
  

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Publications

• Existence of quasilinear relaxation shock profiles in systems with characteristic velocities, with Guy Métivier and Kevin Zumbrun, to appear in Annales Scientifiques de la faculté des sciences de Toulouse, 2011. 


• Nash-Moser iteration and singular perturbations, with Kevin Zumbrun, Annales de l'IHP (analyse non-linéaire) 28 (2011), no. 4, 499-527. 


• Transition to longitudinal instability of detonation waves is generically associated with Hopf bifurcation to time-periodic galloping solutions, with Kevin Zumbrun, Comm. Math. Phys. 302 (2011), no. 1, 1-51. 


• Hopf bifurcation of viscous shock waves in compressible gas dynamics and MHD, with Kevin Zumbrun, Archive for Rational Mechanics and Analysis,  190  (2008),  no. 1, 107--140.


• Galloping instability of viscous shock waves, with Kevin Zumbrun, Physica D, 237  (2008),  no. 10-12, 1553--1601.


• Pointwise Green function bounds and stability of detonation waves, with Gregory Lyng, Mohammedreza Raoofi and Kevin Zumbrun, Journal of Differential Equations 233 (2007), no. 2, 654-698.


• Derivation of the Zakharov equations, Archive for Rational Mechanics and Analysis 184 (2007), no.1, 121-183.


• Relative Poincare-Hopf bifurcation and galloping instabilities for traveling waves, with Kevin Zumbrun, Methods and Applications of Analysis 12 (2005), no. 4, 348-380.


• WKB asymptotics for the Euler-Maxwell equations, Asymptotic Analysis 42 (2005), no. 3-4, 211--250.


• Justification of the Zakharov equations from Klein-Gordon-Wave systems, with Thierry Colin, Géraldine Ebrard and Gérard Gallice, Comm. Part. Diff. Eq. 29 (2004), no. 9-10, 1365--1401.


• Study of a mathematical model for Raman scatterring, with Antoine Bourgeade, Thomas Boucherès, Thierry Colin and Boniface Nkonga, Math. Models Methods Appl. Sci. 14 (2004), no. 2, 217--252.


• The short-wave limit for nonlinear, symmetric, hyperbolic systems, Adv. Diff. Eq.  9 (2004), no. 1, 1-52.


• Problèmes de transmission non coercif dans des polygônes, with Monique Dauge, unpublished note (1997). 

       
   

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CV.

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