7 citations · 9 across the 6 of their papers we have counts for
6 papers
A remark on a generalization of a logarithmic Sobolev inequality to the Holder class
Hassan Ibrahim
In a recent work of the author, a parabolic extension of the elliptic Ogawa type inequality has been established. This inequality is originated from the Brezis-Gallouet-Wainger log…
A critical parabolic Sobolev embedding via Littlewood-Paley decomposition
Hassan Ibrahim
In this paper, we show a parabolic version of the Ogawa type inequality in Sobolev spaces. Our inequality provides an estimate of the norm of a function in terms of it…
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…
Dynamics of dislocation densities in a bounded channel. Part I: smooth solutions to a singular coupled parabolic system
H. Ibrahim, M. Jazar, R. Monneau
We study a coupled system of two parabolic equations in one space dimension. This system is singular because of the presence of one term with the inverse of the gradient of the sol…