most citedDynamics of dislocation densities in a bounded channel. Part I: smooth solutions to a singular coupled parabolic system

7 citations · 9 across the 6 of their papers we have counts for

collaborators

6 papers

math.FA2009

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…

math.FA20092 cited

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…

math.AP2009

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…

math.AP2009

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…

math.AP2009

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…

math.AP20097 cited

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…