Three counterexamples in the theory of inertial manifolds

DOI10.1007/BF02674562zbMath0984.35034OpenAlexW2060784873WikidataQ124937324 ScholiaQ124937324MaRDI QIDQ5942000

Aleksandr V. Romanov

Publication date: 14 May 2002

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02674562

zbMATH Keywords

dissipative semilinear parabolic equationnormal hyperbolicity on the stationary set

Mathematics Subject Classification ID

Abstract parabolic equations (35K90) Inertial manifolds (35B42) Inertial manifolds and other invariant attracting sets of infinite-dimensional dissipative dynamical systems (37L25)

Related Items (11)

Counterexamples to regularity of Mañé projections in the theory of attractors ⋮ Inertial manifolds for the hyperviscous Navier-Stokes equations ⋮ Inertial manifolds for 1D reaction-diffusion-advection systems. II: Periodic boundary conditions ⋮ Inertial manifolds for 3D complex Ginzburg-Landau equations with periodic boundary conditions ⋮ Attractors. Then and now ⋮ Inertial manifolds for the hyperbolic relaxation of semilinear parabolic equations ⋮ Bi-Lipschitz Mané projectors and finite-dimensional reduction for complex Ginzburg–Landau equation ⋮ Kwak transform and inertial manifolds revisited ⋮ A parabolic equation with nonlocal diffusion without a smooth inertial manifold ⋮ Determining functionals and finite-dimensional reduction for dissipative PDEs revisited ⋮ Inertial Manifolds via Spatial Averaging Revisited

Cites Work

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• Geometric theory of semilinear parabolic equations
• Inertial Manifolds for Reaction Diffusion Equations in Higher Space Dimensions
• Twistor spaces and harmonic maps
• Invariant manifolds

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