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Phase-lag heat conduction: decay rates for limit problems and well-posedness
Borgmeyer, Karin; Quintanilla de Latorre, Ramón; Racke, Reinhard
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II; Universitat Politècnica de Catalunya. GRAA - Grup de Recerca en Anàlisi Aplicada
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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.
Peer Reviewed
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
Hyperbolic models in heat conduction
Generalized thermoelasticity
Qualitative aspects
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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