Nonlocal variational problems arising in long wave propagatioN

Free access article

Issue		ESAIM: COCV Volume 5, 2000


Page(s)		501 - 528
DOI		10.1051/cocv:2000119

DOI: 10.1051/cocv:2000119

ESAIM: COCV, November 2000, Vol. 5, 501-528

Nonlocal variational problems arising
in long wave propagatioN

Orlando Lopes
Departamento de Matematica-IMECC-UNICAMP- CP 6065, Campinas SP 13083-970, Brasil; (lopes@ime.unicamp.br)

Received January 20, 2000. Revised August, 2000.

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.

Keywords and phrases: Nonlocal variational problems, stability of traveling waves.

AMS Subject Classification: 35J20, 49J10.

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