Volume 8, 2002
A 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; firstname.lastname@example.org.
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.