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On the structure of layers for singularly perturbed equations in the case of unbounded energy

Published online by Cambridge University Press:  15 August 2002

E. Sanchez–Palencia
E. Sanchez–Palencia*
Affiliation:
Laboratoire de Modélisation en Mécanique, CNRS-Université Pierre et Marie Curie, 4 place Jussieu, 75252 Paris Cedex 05, France; sanchez@lmm.jussieu.fr.
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Abstract

We consider singular perturbation variational problemsdepending on a small parameter ε. The right hand side is suchthat the energydoes not remain bounded as ε → 0. The asymptoticbehavior involves internallayers where most of the energy concentrates. Three examples are addressed,with limits elliptic, parabolic and hyperbolic respectively, whereas theproblems with ε > 0 are elliptic. In the parabolic and hyperboliccases, thepropagation of singularities appear as an integral property after integratingacross the layers.

Keywords

Singular perturbationsunbounded energypropagation of singularities.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 8: A tribute to JL Lions , 2002 , pp. 941 - 963
Copyright
© EDP Sciences, SMAI, 2002

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