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Working paper

On the Hyperbolicity Properties of Inertial Manifolds of Reaction–Diffusion Equations

arxiv.org. math. Cornell University, 2016. No. 1602.08953.
For 3D reaction–diffusion equations, we study the problem of existence or nonexistence of an inertial manifold that is normally hyperbolic or absolutely normally hyperbolic. We present a system of two coupled equations with a cubic nonlinearity which does not admit a normally hyperbolic inertial manifold. An example separating the classes of such equations admitting an inertial manifold and a normally hyperbolic inertial manifold is constructed. Similar questions concerning absolutely normally hy- perbolic inertial manifolds are discussed.