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Title:
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Phase-lag heat conduction: decay rates for limit problems and well-posedness
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Author:
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Borgmeyer, Karin; Quintanilla de Latorre, Ramón; Racke, Reinhard
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Other authors:
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Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II; Universitat Politècnica de Catalunya. GRAA - Grup de Recerca en Anàlisi Aplicada |
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Abstract:
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The final publication is available at Springer via http://dx.doi.org/10.1007/s00028-014-0242-6. |
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Abstract:
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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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Abstract:
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Peer Reviewed |
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Subject(s):
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-Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Equacions en derivades parcials
-Àrees temàtiques de la UPC::Física::Termodinàmica
-Differential equations, Hyperbolic
-Thermodynamics--Mathematics
-Heat--Transmission--Mathematics
-Hyperbolic models in heat conduction
-Stability
-Generalized thermoelasticity
-Qualitative aspects
-Stability
-Waves
-Model
-Termodinàmica -- Matemàtica
-Equacions diferencials hiperbòliques
-Calor -- Transmissió -- Matemàtica
-Classificació AMS::35 Partial differential equations::35L Partial differential equations of hyperbolic type
-Classificació AMS::80 Classical thermodynamics, heat transfer::80A Thermodynamics and heat transfer |
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Rights:
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Document type:
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Article - Submitted version
Article |
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