4 papers
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…
Short time existence and uniqueness in Hölder spaces for the 2D dynamics of dislocation densities
Ahmad El Hajj
In this paper, we study the model of Groma and Balogh describing the dynamics of dislocation densities. This is a two-dimensional model where the dislocation densities satisfy a sy…
Derivation and study of dynamical models of dislocation densities
Ahmad El Hajj, H. Ibrahim, Régis Monneau
In this paper, starting from the microscopic dynamics of isolated dislocations, we explain how to derive formally mean field models for the dynamics of dislocation densities. Essen…
Global continuous solutions to diagonalizable hyperbolic systems with large and monotone data
Ahmad El Hajj, Regis Monneau
In this paper, we study diagonalizable hyperbolic systems in one space dimension. Based on a new gradient entropy estimate, we prove the global existence of a continuous solution,…