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arXiv · 1602.08953

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

A. V. Romanov
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Abstract

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 hyperbolic inertial manifolds are discussed.

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A. V. Romanov. 2016-02-29. On the Hyperbolicity Properties of Inertial Manifolds of Reaction--Diffusion Equations. https://arxiv.org/abs/1602.08953

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