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Local Bifurcations in the Generalized Cahn-Hilliard Equation

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Differential and Difference Equations with Applications (ICDDEA 2019)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 333))

Abstract

A periodic boundary value problem for a generalized Cahn-Hilliard equation is studied. Bifurcation problems are considered. The analysis of these bifurcation problems use the methods of invariant manifold and the Poincare normal forms for the dynamic systems with an infinite-dimensional space of initial conditions. It is proved that this dynamic systems has a local attractor formed by unstable solutions in the sense of Lyapunov definition. Asymptotic formulas for these solutions are obtained.

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Authors and Affiliations

  1. Demidov Yaroslavl State University, Yaroslavl, Russia

    A. Kulikov & D. Kulikov

Authors
  1. A. Kulikov
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  2. D. Kulikov
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Corresponding author

Correspondence to D. Kulikov .

Editor information

Editors and Affiliations

  1. Department of Exact Sciences and Engineering, Military Academy, Lisbon, Portugal

    Sandra Pinelas

  2. Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN, USA

    John R. Graef

  3. Mathematik und Didaktik, Katholische Universität Eichstätt, Eichstätt, Bayern, Germany

    Stefan Hilger

  4. Huazhong University of Science and Technology, Wuhan, Hubei, China

    Peter Kloeden

  5. Department of Electrical and Computer Engineering, Democritus University of Thrace, Xanthi, Xanthi, Greece

    Christos Schinas

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Kulikov, A., Kulikov, D. (2020). Local Bifurcations in the Generalized Cahn-Hilliard Equation. In: Pinelas, S., Graef, J.R., Hilger, S., Kloeden, P., Schinas, C. (eds) Differential and Difference Equations with Applications. ICDDEA 2019. Springer Proceedings in Mathematics & Statistics, vol 333. Springer, Cham. https://doi.org/10.1007/978-3-030-56323-3_14

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