Existencia e estabilidade de ondas viajantes periodicas para alguns modelos dispersivos / Existence and stability of periodic travelling waves for some dispersive models

AUTOR(ES)
DATA DE PUBLICAÇÃO

2009

RESUMO

The goal of this thesis is to study the properties of solutions of some dispersive differential equations. First, we develop a local and global well-posedness theory for the regularized Benjamin-Ono equation in the periodic setting, then, we show that the Cauchy problem for this equation (in both periodic and nonperiodic cases) cannot be solved by an iteration scheme based on the Duhamel formula for negative Sobolev indices. Additionally, a proof of the existence of a smooth curve of periodic travelling wave solutions, for the regularized Benjamin-Ono equation, with fixed minimal period 2L, is given. It is also shown that these solutions are nonlinearly stable in the energy space H1/2per by perturbations of the same wavelength. An extension of the theory developed for the regularized Benjamin-Ono equation is given and as examples it is proved that the periodic wave solutions associated to the Benjamin-Bona-Mahony, modified Benjamin-Bona-Mahony and 4-Benjamin-Bona- Mahony equations are nonlinearly stable in H1per. Finally, we prove the existence and the nonlinear estability of a family of dnoidal wave solutions associated to the Zakharov system. The Floquet theory is used in the last case to obtain the spectral properties required to prove the stability.

ASSUNTO(S)

equações de benjamin-bona-mahony equações de benjamin-ono nonlinear stability sistema de zakharov nonlinear partial differential equations zakharov system equações diferenciais não-lineares benjamin-bona-mahony equations benjamin-ono equations estabilidade não-linear

ACESSO AO ARTIGO

Documentos Relacionados