caa a22 4500 475740416 CHVBK 20180406123458.0 cr unu---uuuuu 170329e20000901xx s 000 0 eng 10.1007/BF02674562 doi (NATIONALLICENCE)springer-10.1007/BF02674562 Romanov A. All-Russia Institute of Scientific and Technical Information, Russian Academy of Sciences, USSR aut Three counterexamples in the theory of inertial manifolds [Elektronische Daten] [A. Romanov] An example of a dissipative semilinear parabolic equation in a Hilbert space without smooth inertial manifolds is constructed. Moreover, the attractor of this equation can be embedded in no finite-dimensionalC 1 invariant submanifold of the phase space. The class of scalar reaction-diffusion equations in bounded domains Ω ⊂ ℝm without inertial manifolds $$\mathcal{M} \subset L^{\text{2}} (\Omega )$$ with the property of absolute normal hyperbolicity on the setE of stationary points of the phase semiflow is described. Such equations may have inertial manifolds with the weaker property of normal hyperbolicity onE. Three-dimensional reaction-diffusion systems without inertial manifolds normally hyperbolic at stationary points are found. Kluwer Academic/Plenum Publishers, 2000 smooth inertial manifold nationallicence dissipative semilinear parabolic equation nationallicence reaction-diffusion equation nationallicence inertial manifold (absolutely) normally hyperbolic on the stationary set nationallicence asymptotic finite-dimensionality nationallicence Mathematical Notes Kluwer Academic Publishers-Plenum Publishers 68/3(2000-09-01), 378-385 0001-4346 68:3<378 2000 68 11006 https://doi.org/10.1007/BF02674562 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02674562 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Romanov A. All-Russia Institute of Scientific and Technical Information, Russian Academy of Sciences, USSR aut NATIONALLICENCE 773 0- Mathematical Notes Kluwer Academic Publishers-Plenum Publishers 68/3(2000-09-01), 378-385 0001-4346 68:3<378 2000 68 11006 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer