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Regular version of the site

Article

On the hyperbolicity properties of inertial manifolds of reaction–diffusion equations

Dynamics of Partial Differential Equations. 2016. Vol. 13. No. 3. P. 263-272.

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.