Research

My research focuses on nonlinear elliptic and parabolic Partial Differentials Equations in general, and more precisely

• Generalized optimal transport and applications to PDEs

• Gradient-flows in metric spaces, calculus of variations

• Degenerate elliptic and parabolic equations and systems (theory and numerics)

• Mathematical modelling for diffusion problems applied to physics and biology

• Free-boundary problems

• Reaction-diffusion equations, front and wave propagation

PhD

In December 2011 I defended my PhD "Models of nonlinear diffusion arising in the theory of Inertial Confinement Fusion", supervised by Jean-Michel Roquejoffre in IMT Univ. Toulouse 3. You can download my dissertation either in French or in English. The jury was composed of

• Jean-Michel Roquejoffre, IMT Toulouse (advisor)

• Olivier Ley, IRMAR and INSA Rennes (referee)

• Alex Kiselev, Duke Univ. (referee)

• Michel Pierre, IRMAR and ENS Rennes (president of the jury)

• Alexeï Novikov, Penn State Univ.

• Raphaël Loubère, IMB Bordeaux

• Mihai Maris, IMT Toulouse

• Paul Clavin, IRPHE Marseille

Undergraduate works

• Masters thesis "Étude d'une classe de solutions de l'équation des milieux poreux" (M2 recherche 2007/2008) supervised by Jean-Michel Roquejoffre, Univ Toulouse 3

• Technical report for my research internship (3 months, summer 2006) "A 2-zonal modes spectral investigation in an ocean-only southern basin" in Institute for Marine and Atmospheric research Utrecht, supervised by Henk A. Dijkstra

• Technical report for my research internship (3months, summer 2005) "Contrôle des systèmes Hamiltoniens, application à la fusion plasmique et système Hénon-Heiles" in Centre de Physique Théorique Marseille, supervised by Michel Vittot and Ricardo Lima

Emergence of chaos and disparition of the KAM tori (Poincaré sections) for the Hénon-Heiles system as the energy E increases