Nonlocal variational problems arising in long wave propagatioN
Departamento de Matematica-IMECC-UNICAMP- CP 6065, Campinas SP 13083-970, Brasil; email@example.com.
Received: August 2000
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.
Mathematics Subject Classification: 35J20 / 49J10
Key words: Nonlocal variational problems / stability of traveling waves.
© EDP Sciences, SMAI, 2000