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Parabolic Problems pp 541–576Cite as

On Conserved Penrose-Fife Type Models

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

Abstract

In this paper we investigate quasilinear parabolic systems of conserved Penrose-Fife type. We show maximal L p -regularity for this problem with inhomogeneous boundary data. Furthermore we prove global existence of a solution, under the assumption that the absolute temperature is bounded from below and above. Moreover, we apply the Lojasiewicz-Simon inequality to establish the convergence of solutions to a steady state as time tends to infinity.

Mathematics Subject Classification (2000). 35K55, 35B38, 35B40, 35B65, 82C26.

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Author information

Authors and Affiliations

  1. Institut für Mathematik, Martin-Luther-Universität Halle-Wittenberg, Theodor-Lieser-Str. 5, D-06120, Halle, Germany

    Jan Prüss & Mathias Wilke

Authors
  1. Jan Prüss
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  2. Mathias Wilke
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Corresponding author

Correspondence to Mathias Wilke .

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

Additional information

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

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Prüss, J., Wilke, M. (2011). On Conserved Penrose-Fife Type Models. 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_27

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