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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 problems depending on a small parameter ε. The right hand side is such that the energy does not remain bounded as ε → 0. The asymptotic behavior involves internal layers where most of the energy concentrates. Three examples are addressed, with limits elliptic, parabolic and hyperbolic respectively, whereas the problems with ε > 0 are elliptic. In the parabolic and hyperbolic cases, the propagation of singularities appear as an integral property after integrating across 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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