We consider singular perturbation variational problems depending on a small parameter . The right hand side is such that the energy does not remain bounded as . 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 are elliptic. In the parabolic and hyperbolic cases, the propagation of singularities appear as an integral property after integrating across the layers.
Keywords: 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},
year = {2002},
publisher = {EDP-Sciences},
volume = {8},
doi = {10.1051/cocv:2002043},
zbl = {1070.35005},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv:2002043/}
}
TY - JOUR AU - Sanchez-Palencia, E. TI - On the structure of layers for singularly perturbed equations in the case of unbounded energy JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2002 SP - 941 EP - 963 VL - 8 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/cocv:2002043/ DO - 10.1051/cocv:2002043 LA - en ID - COCV_2002__8__941_0 ER -
%0 Journal Article %A Sanchez-Palencia, E. %T On the structure of layers for singularly perturbed equations in the case of unbounded energy %J ESAIM: Control, Optimisation and Calculus of Variations %D 2002 %P 941-963 %V 8 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/cocv:2002043/ %R 10.1051/cocv:2002043 %G en %F COCV_2002__8__941_0
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
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