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Archive for Rational Mechanics and Analysis

, Volume 196, Issue 1, pp 71–96 | Cite as

Global Existence for a System of Non-Linear and Non-Local Transport Equations Describing the Dynamics of Dislocation Densities

  • Marco Cannone
  • Ahmad El HajjEmail author
  • Régis Monneau
  • Francis Ribaud
Article

Abstract

In this paper, we study the global in time existence problem for the Groma-Balogh model describing the dynamics of dislocation densities. This model is a two-dimensional model where the dislocation densities satisfy a system of transport equations such that the velocity vector field is the shear stress in the material, solving the equations of elasticity. This shear stress can be expressed as some Riesz transform of the dislocation densities. The main tool in the proof of this result is the existence of an entropy for this system.

Keywords

Dislocation Density Burger Vector Global Existence Orlicz Space Young Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • Marco Cannone
    • 1
  • Ahmad El Hajj
    • 1
    Email author
  • Régis Monneau
    • 1
  • Francis Ribaud
    • 1
  1. 1.Ecole Nationale des Ponts et Chaussees, CERMICSMarne-la-Vallee Cedex 2France

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