Dynamics of Partial Differential Equations
Volume 13 (2016)
On the hyperbolicity properties of inertial manifolds of reaction–diffusion equations
Pages: 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.
reaction–diffusion equations, inertial manifold, normal hyperbolicity
2010 Mathematics Subject Classification
Primary 35B42, 35K57. Secondary 35K90, 35K91.