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Phase-lag heat conduction: decay rates for limit problems and well-posedness

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Abstract

In two recent papers, the authors have studied conditions on the relaxation parameters in order to guarantee the stability or instability of solutions for the Taylor approximations to dual-phase-lag and three-phase-lag heat conduction equations. However, for several limit cases relating to the parameters, the kind of stability was unclear. Here, we analyze these limit cases and clarify whether we can expect exponential or slow decay for the solutions. Moreover, rather general well-posedness results for three-phase-lag models are presented. Finally, the exponential stability expected by spectral analysis is rigorously proved exemplarily.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Konstanz, 78457, Konstanz, Germany

    Karin Borgmeyer & Reinhard Racke

  2. Department of Applied Mathematics 2, UPC Terrassa, Colom 11, 08222, Terrassa, Spain

    Ramón Quintanilla

Authors
  1. Karin Borgmeyer
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  2. Ramón Quintanilla
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  3. Reinhard Racke
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Corresponding author

Correspondence to Reinhard Racke.

Additional information

Ramón Quintanilla: Work of R.Q. is part of the project “Análisis Matemático de las Ecuaciones en Derivadas Parciales de la Termomecánica.” (MTM2013-42004-P) submitted to the Spanish Ministry of Economy and Competitiveness.

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Borgmeyer, K., Quintanilla, R. & Racke, R. Phase-lag heat conduction: decay rates for limit problems and well-posedness. J. Evol. Equ. 14, 863–884 (2014). https://doi.org/10.1007/s00028-014-0242-6

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  • DOI: https://doi.org/10.1007/s00028-014-0242-6

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