Various kinds of sensitive singular perturbations

Nicolas Meunier[1]; Jacqueline Sanchez-Hubert[2]; Évariste Sanchez-Palencia[3]

  • [1] MAP5 Université René Descartes 45 rue des Saints Pères 75006 Paris France
  • [2] Laboratoire de Mécanique Université de Caen Département de Mathématiques 4 boulevard Maréchal Juin 14032 Caen France
  • [3] Laboratoire de Modélisation en Mécanique Université Pierre et Marie Curie (Paris VI) 4 place Jussieu 75252 Paris France

Annales mathématiques Blaise Pascal (2007)

  • Volume: 14, Issue: 2, page 199-242
  • ISSN: 1259-1734

Abstract

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We consider variational problems of P. D. E. depending on a small parameter ε when the limit process ε ↓ 0 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 ε ↓ 0 .

How to cite

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Meunier, Nicolas, Sanchez-Hubert, Jacqueline, and Sanchez-Palencia, Évariste. "Various kinds of sensitive singular perturbations." Annales mathématiques Blaise Pascal 14.2 (2007): 199-242. <http://eudml.org/doc/10546>.

@article{Meunier2007,
abstract = {We consider variational problems of P. D. E. depending on a small parameter $\varepsilon $ when the limit process $\varepsilon \downarrow 0$ 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 $\varepsilon \downarrow 0$.},
affiliation = {MAP5 Université René Descartes 45 rue des Saints Pères 75006 Paris France; Laboratoire de Mécanique Université de Caen Département de Mathématiques 4 boulevard Maréchal Juin 14032 Caen France; Laboratoire de Modélisation en Mécanique Université Pierre et Marie Curie (Paris VI) 4 place Jussieu 75252 Paris France},
author = {Meunier, Nicolas, Sanchez-Hubert, Jacqueline, Sanchez-Palencia, Évariste},
journal = {Annales mathématiques Blaise Pascal},
keywords = {highly pathological asymptotic behavior; analytical functionals; complexification},
language = {eng},
month = {7},
number = {2},
pages = {199-242},
publisher = {Annales mathématiques Blaise Pascal},
title = {Various kinds of sensitive singular perturbations},
url = {http://eudml.org/doc/10546},
volume = {14},
year = {2007},
}

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
DA - 2007/7//
PB - Annales mathématiques Blaise Pascal
VL - 14
IS - 2
SP - 199
EP - 242
AB - We consider variational problems of P. D. E. depending on a small parameter $\varepsilon $ when the limit process $\varepsilon \downarrow 0$ 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 $\varepsilon \downarrow 0$.
LA - eng
KW - highly pathological asymptotic behavior; analytical functionals; complexification
UR - http://eudml.org/doc/10546
ER -

References

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