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Collectanea Mathematica

, Volume 69, Issue 3, pp 315–336 | Cite as

\(C^{1,\theta }\)-Estimates on the distance of inertial manifolds

  • José M. Arrieta
  • Esperanza Santamaría
Article

Abstract

In this paper we obtain \(C^{1,\theta }\)-estimates on the distance of inertial manifolds for dynamical systems generated by evolutionary parabolic type equations. We consider the situation where the systems are defined in different phase spaces and we estimate the distance in terms of the distance of the resolvent operators of the corresponding elliptic operators and the distance of the nonlinearities of the equations.

Keywords

Inertial manifolds Evolution equations Perturbations 

Mathematics Subject Classification

35B42 35K90 

Notes

Acknowledgements

We appreciate the carefull comments of the referee that led to a better exposition of the results.

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Copyright information

© Universitat de Barcelona 2018

Authors and Affiliations

  1. 1.Departamento de Análisis Matemático y Matemática AplicadaUniversidad Complutense de MadridMadridSpain
  2. 2.Instituto de Ciencias MatemáticasCSIC-UAM-UC3M-UCMMadridSpain
  3. 3.Universidad a Distancia de MadridMadridSpain

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