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Asymptotic stability via the Krein-Rutman theorem for singularly perturbed parabolic periodic dirichlet problems

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Abstract

We consider singularly perturbed semilinear parabolic periodic problems and assume the existence of a family of solutions. We present an approach to establish the exponential asymptotic stability of these solutions by means of a special class of lower and upper solutions. The proof is based on a corollary of the Krein-Rutman theorem.

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Authors and Affiliations

  1. Faculty of Physics, M.V. Lomonosov Moscow State University, Leninskie Gory, Moscow, 119991, Russia

    N. N. Nefedov

  2. Institut für Mathematik, Humboldt-Universität zu Berlin, Unter den Linden 6, D-10099, Berlin, Germany

    L. Recke

  3. Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117, Berlin, Germany

    K. R. Schneider

Authors
  1. N. N. Nefedov
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  2. L. Recke
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  3. K. R. Schneider
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Corresponding author

Correspondence to N. N. Nefedov.

Additional information

This work is partially supported by RFBR, pr. 08-01-00413, and by the program of cooperation of Lomonosov Moscow State University and Humboldt-Universität zu Berlin.

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Nefedov, N.N., Recke, L. & Schneider, K.R. Asymptotic stability via the Krein-Rutman theorem for singularly perturbed parabolic periodic dirichlet problems. Regul. Chaot. Dyn. 15, 382–389 (2010). https://doi.org/10.1134/S1560354710020231

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  • DOI: https://doi.org/10.1134/S1560354710020231

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