76 citations · 363 across the 36 of their papers we have counts for
9 papers · 1 filter
Homogenization of accelerated Frenkel-Kontorova models with types of particles
Nicolas Forcadel, Cyril Imbert, Régis Monneau
We consider systems of ODEs that describe the dynamics of particles. Each particle satisfies a Newton law (including the acceleration term) where the force is created by the intera…
Diagonal hyperbolic systems with large and monotone data Part I: Global continuous solutions
Ahmad El Hajj, Régis Monneau
In this paper, we study diagonal hyperbolic systems in one space dimension. Based on a new gradient entropy estimate, we prove the global existence of a continuous solution, for la…
Homogenization of dislocation dynamics
A. El Hajj, H. Ibrahim, R. Monneau
In this paper we consider the dynamics of dislocations with the same Burgers vector, contained in the same glide plane, and moving in a material with periodic obstacles. We study t…
On the rate of convergence in periodic homogenization of scalar first-order ordinary differential equations
H. Ibrahim, R. Monneau
In this paper, we study the rate of convergence in periodic homogenization of scalar ordinary differential equations. We provide a quantitative error estimate between the solutions…
On a parabolic logarithmic Sobolev inequality
H. Ibrahim, R. Monneau
In order to extend the blow-up criterion of solutions to the Euler equations, Kozono and Taniuchi have proved a logarithmic Sobolev inequality by means of isotropic (elliptic) $BMO…
Dynamics of dislocation densities in a bounded channel. Part II: existence of weak solutions to a singular Hamilton-Jacobi/parabolic strongly coupled system
H. Ibrahim, M. Jazar, R. Monneau
We study a strongly coupled system consisting of a parabolic equation and a singular Hamilton-Jacobi equation in one space dimension. This system describes the dynamics of dislocat…