Derivation and study of dynamical models of dislocation densitiesReport as inadecuate




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1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans 2 CERMICS - Centre d-Enseignement et de Recherche en Mathématiques et Calcul Scientifique 3 CERMICS - Centre d-Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique

Abstract : 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. Essentially these models are tranport equations, coupled with the equations of elasticity. Rigorous results of existence of solutions are presented for some of these models and the main ideas of the proofs are given.

Keywords : dynamics of dislocation densities Cauchy-s problem non-linear transport equations non-local transport equations hyperbolic equations BMO estimate dynamics of dislocation densities.





Author: Ahmad El Hajj - H. Ibrahim - Régis Monneau -

Source: https://hal.archives-ouvertes.fr/



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