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Hassan Ali Ibrahim

Full professor
Mathematics department - Section I - Hadath
Speciality: Mathematics
Specific Speciality: Analysis; Partial Differential Equations
Interests: Cinema and music concerts

Positions
2009 - present : Professor

Lebanese University
Hadath

2008 - 2009 : ATER

Université Paris Dauphine
Paris

Teaching 6 Taught Courses
(2014-2015) MEDP 511 - Hamilton-Jacobi equations and viscosity solutions

M2 Partial Differential Equations and Numerical Analysis

(2014-2015) Math 106 - Functions of Several Variables & Vector Functions

BS Mathematics

(2014-2015) Math 407 - Partial differential equations

M1 Mathematics

(2014-2015) Math 277 - Mathematics for informatics

BS Computer Sciences

(2014-2015) Math 209 - Metric Topology II and complex analysis

BS Mathematics

(2014-2015) Math 306 - Integration II

BS Mathematics

Education
2005 - 2008: Doctorat

Ecoles des Ponts - ParisTech
Mathematics and Informatics

2004 - 2005: DEA

Lebanese University
PDEs and nonlinear analysis

1999 - 2003: Masters

Lebanese University
Mathematics

Publications 16 publications
H. Ibrahim, R. Monneau Reduced ODE dynamics as formal relativistic asymptotics of a PeierlsNabarro model European Journal of Applied Mathematics 2014

H. Ibrahim, S. Zabad Existence of viscosity solution for a singular Hamilton-Jacobi equation Arab J Math Sci 2014

B. Barakeh, A. Z. Fino, H. Ibrahim Decay of mass for fractional evolution equation with memory term Quart. Appl. Math. 2013

A. Z. Fino, H. Ibrahim Analytical solution for a generalized space-time fractional telegraph equation Math. Methods Appl. Sci. 2013

A. Z. Fino, H. Ibrahim, R. Monneau The Peierls-Nabarro model as a limit of a Frenkel- Kontorova model Journal of Differential Equations 2012

H. Ibrahim A generalisation of a logarithmic Sobolev inequality to the Holder class Journal of Function Spaces and Applications 2012

H. Ibrahim Critical parabolic Sobolev embeddings via Littlewood-Paley decomposition International Mathematical Forum 2012

H. Ibrahim, M. Jazar, R. Monneau Dynamics of dislocation densities in a bounded channel. Part I: smooth solutions to a singular coupled parabolic system Commun. Pure Appl. Anal. 2010

H. Ibrahim, R. Monneau On the rate of convergence in homogenization of scalar SIAM J. Math. Anal. 2010

H. Ibrahim Existence and uniqueness for a nonlinear parabolic/Hamilton-Jacobi coupled system describing the dynamics of dislocation densities Ann. I. H. Poincaré Anal. Non Linéaire 2009

H. Ibrahim, R. Monneau On a parabolic logarithmic Sobolev inequality J. Funct. Anal. 2009

H. Ibrahim, M. Jazar, R. Monneau Dynamics of dislocation densities in a bounded channel. Part II: existence of weak solutions to a singular Hamilton-Jacobi/parabolic strongly coupled system Communications in Partial Di 2009

A. El Hajj, H. Ibrahim, R. Monneau Dislocation dynamics: from microscopic models to macroscopic crystal plasticity Continuum Mech. Thermodyn. 2009

A. El Hajj, H. Ibrahim, R. Monneau Derivation and study of dynamical models of dislocation densities ESAIM : PROCEEDINGS 2009

A. El Hajj, H. Ibrahim, R. Monneau Homogenization of dislocation dynamics IOP Conf. Series, Materials Science and Engineering 2009

H. Ibrahim, M. Jazar, R. Monneau Global existence of solutions to a singular parabolic/Hamilton-Jacobi coupled system with Dirichlet conditions C. R. Acad. Sci. Paris, Ser. I 2008

Supervision 1 Supervised Student
Analysis of strongly coupled singular parabolic system of dislocation dynamics

Vivian Hussein Rizik
Master M2 Thesis: Partial Differential Equations and Numerical Analysis in 2015

Analysis of parabolic/Hamilton-Jacobi systems modelling the dynamics of dislocation densities in a bounded channel

Mohammad Al-Haj
M2 Mathematics

We study a mathematical model describing the dynamics of dislocation densities in crystal. This model is expressed as a 1D system of a parabolic equation and a first order Hamilton- Jacobi equation that are coupled together. We examine an associated Dirichlet boundary value problem. We prove the existence and uniqueness of a viscosity solution among those assuming a lower-bound on their gradient for all time including the initial time. Moreover, we show the existence of a viscosity solution when we have no such restriction on the initial data. We also state a result of existence and uniqueness of entropy solution for the initial value problem of the system obtained by spatial derivation. The uniqueness of this entropy solution holds in the class of bounded-from-below solutions. In order to prove our results on the bounded domain, we use an "extension and restriction" method, and we exploit a relation between scalar conservation laws and Hamilton-Jacobi equations, mainly to get our gradient estimates.

Languages
Arabic

Native or bilingual proficiency

English

Full professional proficiency

French

Professional working proficiency