Hassan IBRAHIM

Lebanese University
Faculty of Sciences
Section I: Hadath

and

Lebanese International University

Research themes
Singular parabolic systems of PDEs. Harmonic analysis and logarithmic Sobolev inequalities. Viscosity solutions for Hamilton-Jacobi equations. Entropy solutions for scalar conservation laws. Error estimates in homogenization of ODEs. Numerical methods: fast Marching method for transport equations.
Ph. D. thesis
Ph. D. in Applied Mathematics from ENPC "Ecole des Ponts ParisTech" (thesis defended on June 30th, 2008 - graduated with highest honors and the congratulations of the jury). Ph. D. Dissertation: Analysis of parabolic/Hamilton-Jacobi systems modelizing the dynamics of dislocation densities in a bounded domain. Jury: G. Barles (examinator), J. Droniou (Ph. D. reporter), M. Effendiev (examinator), M. Jazar (Ph. D. co-advisor), R. Monneau (Ph. D. advisor), N. Nassif (examinator), B. Perthame (Ph. D. reporter), J.-L. Vázquez (president of the jury).
Publications
1. Existence and uniqueness for a nonlinear parabolic/Hamilton-Jacobi coupled system describing the dynamics of dislocation densities, Ann. I. H. Poincaré Anal. Non Linéaire 26 (2009) 415-435. 2. (with M. Jazar and R. Monneau) Global existence of solutions to a singular parabolic/Hamilton-Jacobi coupled system with Dirichlet conditions, C. R. Acad. Sci. Paris, Ser. I 346 (2008) 945-950. 3. (with R. Monneau) On a parabolic logarithmic Sobolev inequality, J. Funct. Anal. 257 (2009) 903-930. 4. (with M. Jazar and R. Monneau) Dynamics of dislocation densities in a bounded channel. Part II: existence of weak solutions to a singular parabolic/Hamilton-Jacobi strongly coupled system, Communications in Partial Differential Equations, 34 (2009), no. 8, 889-917. 5. (with A. El Hajj and R. Monneau) Dislocation dynamics: from microscopic models to macroscopic crystal plasticity, Continuum Mech. Thermodyn. 21 (2009), no. 2, 109-123. 6. (with A. El Hajj and R. Monneau) Derivation and study of dynamical models of dislocation densities, ESAIM: PROCEEDINGS, May 2009, Vol. 27, p. 227-239. 7. (with A. El Hajj and R. Monneau) Homogenization of dislocation dynamics, IOP Conf. Series: Materials Science and Engineering 3 (2009) 012023. 8. (with M. Jazar and R. Monneau) Dynamics of dislocation densities in a bounded channel. Part I: smooth solutions to a singular parabolic system, Communications on Pure and Applied Analysis, Volume 9, Number 3, May 2010. 9. (with R. Monneau) On the rate of convergence in periodic homogenization of scalar first-order ODEs, accepted for publication in SIAM Journal on Mathematical Analysis. 10. (with A. Fino and R. Monneau) The Peierls-Nabarro model as a limit of a Frenkel-Kontorova model, in preparation.
See some numerical simulations
My CV