A variational convergence for bifunctionals. Application to a model of strong junction

Anne-Laure Bessoud

doi:10.3934/dcdss.2012.5.399

Article Contents

2012, Volume 5, Issue 3: 399-417. Doi: 10.3934/dcdss.2012.5.399

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A variational convergence for bifunctionals. Application to a model of strong junction

Anne-Laure Bessoud^1,

1.
IMATH, Université du Sud Toulon-Var, BP 20132 - 83957 La Garde Cedex

Received: August 2010

Revised: September 2010

Published: June 2012

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Abstract

We introduce a notion of variational convergence for bifunctionals in an abstract setting. Then we apply this convergence to the asymptotic analysis of a junction problem in order to capture the gradient oscillations in the joint by considering the energy functional as a bifunctional of Sobolev-function/Young measure arguments. The well known asymptotic model described in terms of Sobolev-functions is obtained by eliminating the Young-measure argument considered as an internal variable through a marginal map. Furthermore, the surface energy of the classical model can be considered as a relaxation of a Dirichlet condition.

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Mathematics Subject Classification: 49J45, 74N15, 35B40.

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