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Reduction Principle and Asymptotic Phase for Center Manifolds of Parabolic Systems with Nonlinear Boundary Conditions

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Abstract

We prove the reduction principle and study other attractivity properties of the center and center-unstable manifolds in the vicinity of a steady-state solution for quasilinear systems of parabolic partial differential equations with fully nonlinear boundary conditions on bounded or exterior domains.

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Notes

  1. We corrected in formula (2.26) a misprint found in [18].

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Acknowledgments

Supported by the MIUR (Italy) and the MCI (Spain), by the US National Science Foundation under Grant NSF DMS-1067929 and the Research Board and Research Council of the University of Missouri, and by the Deutsche Forschungsgemeinschaft.

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Authors and Affiliations

  1. Dipartimento di Sistemi e Informatica, Universita di Firenze, Florence, 50139, Italy

    Russell Johnson

  2. Department of Mathematics, University of Missouri, Columbia, MO , 65211, USA

    Yuri Latushkin

  3. Department of Mathematics, Karlsruhe Institute of Technology, 76128 , Karlsruhe, Germany

    Roland Schnaubelt

Authors
  1. Russell Johnson
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  2. Yuri Latushkin
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  3. Roland Schnaubelt
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Correspondence to Yuri Latushkin.

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Johnson, R., Latushkin, Y. & Schnaubelt, R. Reduction Principle and Asymptotic Phase for Center Manifolds of Parabolic Systems with Nonlinear Boundary Conditions. J Dyn Diff Equat 26, 243–266 (2014). https://doi.org/10.1007/s10884-014-9360-7

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  • DOI: https://doi.org/10.1007/s10884-014-9360-7

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