Nonlocal variational problems arising in long wave propagatioN

Orlando Lopes

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • Volume: 5, page 501-528
  • ISSN: 1292-8119

Abstract

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In this paper we study the existence of minimizer for certain constrained variational problems given by functionals with nonlocal terms. This type of functionals are first integrals of evolution equations describing long wave propagation and the existence of minimizer gives the existence and the stability of traveling waves for these equations. Due to loss of compactness, the major problem is to prevent dichotomy of minimizing sequences. Our approach is an alternative to the concentration-compactness method and it allows us to deal with some functionals for which the verification of the strict subadditivity seems to be difficult.

How to cite

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Lopes, Orlando. "Nonlocal variational problems arising in long wave propagatioN." ESAIM: Control, Optimisation and Calculus of Variations 5 (2010): 501-528. <http://eudml.org/doc/197302>.

@article{Lopes2010,
abstract = { In this paper we study the existence of minimizer for certain constrained variational problems given by functionals with nonlocal terms. This type of functionals are first integrals of evolution equations describing long wave propagation and the existence of minimizer gives the existence and the stability of traveling waves for these equations. Due to loss of compactness, the major problem is to prevent dichotomy of minimizing sequences. Our approach is an alternative to the concentration-compactness method and it allows us to deal with some functionals for which the verification of the strict subadditivity seems to be difficult. },
author = {Lopes, Orlando},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Nonlocal variational problems; stability of traveling waves.; stability of traveling waves; constrained variational problems},
language = {eng},
month = {3},
pages = {501-528},
publisher = {EDP Sciences},
title = {Nonlocal variational problems arising in long wave propagatioN},
url = {http://eudml.org/doc/197302},
volume = {5},
year = {2010},
}

TY - JOUR
AU - Lopes, Orlando
TI - Nonlocal variational problems arising in long wave propagatioN
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 5
SP - 501
EP - 528
AB - In this paper we study the existence of minimizer for certain constrained variational problems given by functionals with nonlocal terms. This type of functionals are first integrals of evolution equations describing long wave propagation and the existence of minimizer gives the existence and the stability of traveling waves for these equations. Due to loss of compactness, the major problem is to prevent dichotomy of minimizing sequences. Our approach is an alternative to the concentration-compactness method and it allows us to deal with some functionals for which the verification of the strict subadditivity seems to be difficult.
LA - eng
KW - Nonlocal variational problems; stability of traveling waves.; stability of traveling waves; constrained variational problems
UR - http://eudml.org/doc/197302
ER -

References

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