On the structure of layers for singularly perturbed equations in the case of unbounded energy
ESAIM: Control, Optimisation and Calculus of Variations, Tome 8 (2002) , pp. 941-963.

We consider singular perturbation variational problems depending on a small parameter $\epsilon$. The right hand side is such that the energy does not remain bounded as $\epsilon \to 0$. 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 $\epsilon >0$ are elliptic. In the parabolic and hyperbolic cases, the propagation of singularities appear as an integral property after integrating across the layers.

DOI : https://doi.org/10.1051/cocv:2002043
Classification : 35A35,  35B25,  35B40
Mots clés : singular perturbations, unbounded energy, propagation of singularities
@article{COCV_2002__8__941_0,
author = {Sanchez-Palencia, E.},
title = {On the structure of layers for singularly perturbed equations in the case of unbounded energy},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {941--963},
publisher = {EDP-Sciences},
volume = {8},
year = {2002},
doi = {10.1051/cocv:2002043},
zbl = {1070.35005},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/cocv:2002043/}
}
Sanchez-Palencia, E. On the structure of layers for singularly perturbed equations in the case of unbounded energy. ESAIM: Control, Optimisation and Calculus of Variations, Tome 8 (2002) , pp. 941-963. doi : 10.1051/cocv:2002043. http://archive.numdam.org/articles/10.1051/cocv:2002043/

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