Calculus of Variations and Geometric Measure Theory
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A. Briani - R. Monneau

Time-homogenization of a first order system arising in the modelling of the dynamics of dislocation densities

created by briani on 19 Nov 2008
modified on 11 Mar 2009

[BibTeX]

Published Paper

Inserted: 19 nov 2008
Last Updated: 11 mar 2009

Journal: C. R. Acad. Sci. Paris, Ser I
Volume: 347
Pages: 231-236
Year: 2009

Abstract:

In this Note we are interested in the dynamics of dislocation densities in a material submitted to a time periodic stress. The dislocation densities solve a set of two coupled first order equations of Burgers' type. Our main aim is to give a description of the long time behaviour of those densities. By an homogenization procedure in the framework of viscosity solutions, we obtain that at the limit, the dislocation densities fulfills a single diffusion equation.


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