On the construction of inertial manifolds under symmetry constraints II: O(2) constraint and inertial manifolds on thin domains

  1. Aníbal Rodríguez-Bernal 1
  1. 1 Universidad Complutense de Madrid
    info

    Universidad Complutense de Madrid

    Madrid, España

    ROR 02p0gd045

Revista:
Journal de Mathématiques Pures et Appliquées

ISSN: 0021-7824

Año de publicación: 1993

Volumen: 72

Número: 1

Páginas: 57-79

Tipo: Artículo

Otras publicaciones en: Journal de Mathématiques Pures et Appliquées

Resumen

On a model example, the Kuramoto-Velarde equation, which includes the Kuramoto-Sivashin-sky and the Cahn-Hilliard models, and under suitable and reasonable hypothesis, we show the dimension and determining modes of inertial manifolds for several classes of solutions. We also give bounds for the dimensions of inertial manifolds of the full system as a parameter is varied. The results are pointed out to be almost model-independent. The same ideas are also applied to a class of parabolic equations in higher space dimension, obtaining results about inertial manifolds on thin and small domains.