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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.

Information

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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