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On the hyperbolicity properties of inertial manifolds of reaction–diffusion equations
Dynamics of Partial Differential Equations ( IF 1.1 ) Pub Date : 2016-01-01 , DOI: 10.4310/dpde.2016.v13.n3.a4
A. V. Romanov 1
Affiliation  

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。
更新日期:2016-01-01
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