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

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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https://hal.archives-ouvertes.fr/hal-00339921
Contributor : Ariela Briani Connect in order to contact the contributor
Submitted on : Wednesday, November 19, 2008 - 2:18:55 PM
Last modification on : Wednesday, May 11, 2022 - 12:06:05 PM
Long-term archiving on: : Monday, June 7, 2010 - 9:43:25 PM

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Ariela Briani, Régis Monneau. Time-homogenization of a first order system arising in the modelling of the dynamics of dislocation densities. Comptes rendus de l'Académie des sciences. Série I, Mathématique, 2009, 347, pp.231-236. ⟨10.1016/j.crma.2009.01.006⟩. ⟨hal-00339921⟩

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