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We consider variational problems of P. D. E. depending on a small parameter when the limit process implies vanishing of the higher order terms. The perturbation problem is said to be sensitive when the energy space of the limit problem is out of the distribution space, so that the limit problem is out of classical theory of P. D. E. We present here a review of the subject, including abstract convergence theorems and two very different model problems (the second one is presented for the first time). For each one we prove the sensitive character and we give a formal asymptotics for the behavior .
Meunier, Nicolas 1 ; Sanchez-Hubert, Jacqueline 2 ; Sanchez-Palencia, Évariste 3
@article{AMBP_2007__14_2_199_0,
author = {Meunier, Nicolas and Sanchez-Hubert, Jacqueline and Sanchez-Palencia, \'Evariste},
title = {Various kinds of sensitive singular perturbations},
journal = {Annales math\'ematiques Blaise Pascal},
pages = {199--242},
publisher = {Annales math\'ematiques Blaise Pascal},
volume = {14},
number = {2},
year = {2007},
doi = {10.5802/ambp.233},
zbl = {1153.35011},
mrnumber = {2369872},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.5802/ambp.233/}
}
TY - JOUR AU - Meunier, Nicolas AU - Sanchez-Hubert, Jacqueline AU - Sanchez-Palencia, Évariste TI - Various kinds of sensitive singular perturbations JO - Annales mathématiques Blaise Pascal PY - 2007 SP - 199 EP - 242 VL - 14 IS - 2 PB - Annales mathématiques Blaise Pascal UR - http://geodesic.mathdoc.fr/articles/10.5802/ambp.233/ DO - 10.5802/ambp.233 LA - en ID - AMBP_2007__14_2_199_0 ER -
%0 Journal Article %A Meunier, Nicolas %A Sanchez-Hubert, Jacqueline %A Sanchez-Palencia, Évariste %T Various kinds of sensitive singular perturbations %J Annales mathématiques Blaise Pascal %D 2007 %P 199-242 %V 14 %N 2 %I Annales mathématiques Blaise Pascal %U http://geodesic.mathdoc.fr/articles/10.5802/ambp.233/ %R 10.5802/ambp.233 %G en %F AMBP_2007__14_2_199_0
Meunier, Nicolas; Sanchez-Hubert, Jacqueline; Sanchez-Palencia, Évariste. Various kinds of sensitive singular perturbations. Annales mathématiques Blaise Pascal, Tome 14 (2007) no. 2, pp. 199-242. doi: 10.5802/ambp.233
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