Volume 8, 2002A tribute to JL Lions
|Page(s)||941 - 963|
|Published online||15 August 2002|
On the structure of layers for singularly perturbed equations in the case of unbounded energy
Laboratoire de Modélisation en Mécanique, CNRS-Université Pierre et Marie Curie, 4 place Jussieu, 75252 Paris Cedex 05, France; email@example.com.
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.
Mathematics Subject Classification: 35A35 / 35B25 / 35B40
Key words: Singular perturbations / unbounded energy / propagation of singularities.
© EDP Sciences, SMAI, 2002
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