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Linearized Stability for Nonlinear Partial Differential Delay Equations

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Parabolic Problems

Part of the book series: Progress in Nonlinear Differential Equations and Their Applications ((PNLDE,volume 80))

Abstract

The object of the paper are partial differential delay equations of the form \( \dot{u}(t)+Bu(t)\ni\,F(u_{t}),\,t \geq 0,\,u_{0} = \varphi \), with \( B\,\subset\,X\,\times\,X\,\omega \)-accretive in a Banach space X. We extend the principle of linearized stability around an equilibrium from the semilinear case, with B linear, to the fully nonlinear case, with B having a linear ‘resolvent-differential’ at the equilibrium.

Mathematics Subject Classification (2000). Primary 35R10, 47J35; Secondary 47H06, 47H20.

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Authors and Affiliations

  1. Fakultät für Mathematik, Universität Duisburg-Essen, D-45117, Essen, Germany

    Wolfgang M. Ruess

Authors
  1. Wolfgang M. Ruess
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Correspondence to Wolfgang M. Ruess .

Editor information

Editors and Affiliations

  1. Inst. Angewandte Mathematik, Leibniz Universität Hannover, Welfengarten 1, Hannover, 30167, Germany

    Joachim Escher

  2. School of Physical Sciences, Dept. Mathematics, University of California, Irvine, Irvine, 92697-3875, California, USA

    Patrick Guidotti

  3. , Fachbereich Mathematik, TU Darmstadt, Schlossgartenstr 7, Darmstadt, 64289, Germany

    Matthias Hieber

  4. Inst. Applied Mathematics & Mechanics, Warsaw University, ul. Banacha 2, Warszawa, 02-097, Poland

    Piotr Mucha

  5. , FB Mathematik und Informatik, Universität Halle-Wittenberg, Theodor-Lieser-Strasse 5, Halle, 06099, Germany

    Jan W. Prüss

  6. 3-4-1, Ohkubo Shinjuku-ku, Tokyo, 169-8555, Japan

    Yoshihiro Shibata

  7. , Deparment of Mathematics, Vanderbilt University, 1326 Stevenson Center, Nashville, TN 37240, USA

    Gieri Simonett

  8. Inst. Angewandte Mathematik, Leibniz Universität Hannover, Welfengarten 1, Hannover, 30167, Germany

    Christoph Walker

  9. Fac. Mathematics & Information Sciences, Warsaw University of Technology, pl. Politechniki 1, Warszawa, 00-661, Poland

    Wojciech Zajaczkowski

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Dedicated to Herbert Amann on the occasion of his 70th birthday

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Ruess, W.M. (2011). Linearized Stability for Nonlinear Partial Differential Delay Equations. In: Escher, J., et al. Parabolic Problems. Progress in Nonlinear Differential Equations and Their Applications, vol 80. Springer, Basel. https://doi.org/10.1007/978-3-0348-0075-4_29

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