On stabilization and control for the critical Klein-Gordon equation on a 3-D compact manifold

Camille Laurent[1]

  • [1] Laboratoire de Mathématiques d’Orsay, UMR 8628 CNRS, Université Paris-Sud, Orsay Cedex, F-91405

Journées Équations aux dérivées partielles (2011)

  • Volume: 260, Issue: 5, page 1-17
  • ISSN: 0752-0360

Abstract

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We study the internal stabilization and control of the critical nonlinear Klein-Gordon equation on 3-D compact manifolds. Under a geometric assumption slightly stronger than the classical geometric control condition, we prove exponential decay for some solutions bounded in the energy space but small in a lower norm. The proof combines profile decomposition and microlocal arguments. This profile decomposition, analogous to the one of Bahouri-Gérard [2] on ℝ 3 , is performed by taking care of possible geometric effects. It uses some results of S. Ibrahim [16] on the behavior of concentrating waves on manifolds.

How to cite

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Laurent, Camille. "On stabilization and control for the critical Klein-Gordon equation on a 3-D compact manifold." Journées Équations aux dérivées partielles 260.5 (2011): 1-17. <http://eudml.org/doc/219800>.

@article{Laurent2011,
abstract = {We study the internal stabilization and control of the critical nonlinear Klein-Gordon equation on 3-D compact manifolds. Under a geometric assumption slightly stronger than the classical geometric control condition, we prove exponential decay for some solutions bounded in the energy space but small in a lower norm. The proof combines profile decomposition and microlocal arguments. This profile decomposition, analogous to the one of Bahouri-Gérard [2] on $\mathbb\{R\}^3$, is performed by taking care of possible geometric effects. It uses some results of S. Ibrahim [16] on the behavior of concentrating waves on manifolds.},
affiliation = {Laboratoire de Mathématiques d’Orsay, UMR 8628 CNRS, Université Paris-Sud, Orsay Cedex, F-91405},
author = {Laurent, Camille},
journal = {Journées Équations aux dérivées partielles},
keywords = {concentration-compacyness; internal stabilization and control; exponential decay; profile decomposition; microlocal arguments},
language = {eng},
month = {6},
number = {5},
pages = {1-17},
publisher = {Groupement de recherche 2434 du CNRS},
title = {On stabilization and control for the critical Klein-Gordon equation on a 3-D compact manifold},
url = {http://eudml.org/doc/219800},
volume = {260},
year = {2011},
}

TY - JOUR
AU - Laurent, Camille
TI - On stabilization and control for the critical Klein-Gordon equation on a 3-D compact manifold
JO - Journées Équations aux dérivées partielles
DA - 2011/6//
PB - Groupement de recherche 2434 du CNRS
VL - 260
IS - 5
SP - 1
EP - 17
AB - We study the internal stabilization and control of the critical nonlinear Klein-Gordon equation on 3-D compact manifolds. Under a geometric assumption slightly stronger than the classical geometric control condition, we prove exponential decay for some solutions bounded in the energy space but small in a lower norm. The proof combines profile decomposition and microlocal arguments. This profile decomposition, analogous to the one of Bahouri-Gérard [2] on $\mathbb{R}^3$, is performed by taking care of possible geometric effects. It uses some results of S. Ibrahim [16] on the behavior of concentrating waves on manifolds.
LA - eng
KW - concentration-compacyness; internal stabilization and control; exponential decay; profile decomposition; microlocal arguments
UR - http://eudml.org/doc/219800
ER -

References

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