On the construction of inertial manifolds under symmetry constraints II: O(2) constraint and inertial manifolds on thin domains
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1
Universidad Complutense de Madrid
info
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.