Inertial manifolds for nonautonomous infinite dimensional dynamical systems
The main goal of this paper is to construct inertial manifolds for nonautonomous infinite dimensional dynamical systems. Note that at present there exist numerous results describing the long time behaviour of such systems in terms of uniform global attractors. However, the attractor is a complicated set, in general. Therefore it seems to be quite reasonable to describe the long time behaviour of nonautonomous infinite dimensional dynamical systems by finite dimensional smooth manifolds. Under some natural conditions (including the spectral gap condition) the authors prove the existence of inertial manifolds for a class of nonautonomous evolution equations.
nonautonomous infinite dimensional dynamical systems
scientific article; zbMATH DE number 1292903
scientific article