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.

中文翻译：

---

关于反应扩散方程惯性流形的双曲性质

对于 3D 反应-扩散方程，我们研究通常为双曲或绝对常双曲的惯性流形是否存在的问题。我们提出了一个具有三次非线性的两个耦合方程的系统，它不允许正常双曲惯性流形。构造了一个示例，该示例将允许惯性流形和正常双曲惯性流形的此类方程的类分开。讨论了关于绝对正态双曲惯性流形的类似问题。