Downloads provided by UsageCountsPhase-lag heat conduction: decay rates for limit problems and well-posedness
Copyright policy ) Borgmeyer, Karin; Quintanilla de Latorre, Ramón; Racke, Reinhard;
Phase-lag heat conduction: decay rates for limit problems and well-posedness
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.
The final publication is available at Springer via http://dx.doi.org/10.1007/s00028-014-0242-6.
Peer Reviewed
Spain, Germany
Differential equations, Àrees temàtiques de la UPC::Física::Termodinàmica, :35 Partial differential equations::35L Partial differential equations of hyperbolic type [Classificació AMS], :Matemàtiques i estadística::Equacions diferencials i integrals::Equacions en derivades parcials [Àrees temàtiques de la UPC], Termodinàmica -- Matemàtica, Classificació AMS::80 Classical thermodynamics, hyperbolic models in heat conduction, :Física::Termodinàmica [Àrees temàtiques de la UPC], Heat--Transmission--Mathematics, info:eu-repo/classification/ddc/510, Exponential Stability, Hyperbolic, Equacions diferencials hiperbòliques, Calor -- Transmissió -- Matemàtica, Classificació AMS::35 Partial differential equations::35L Partial differential equations of hyperbolic type, Qualitative aspects, Generalized thermoelasticity, :80 Classical thermodynamics, heat transfer::80A Thermodynamics and heat transfer [Classificació AMS], Asymptotic behavior of solutions to PDEs, dual-phase-lag, Thermodynamics--Mathematics, Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Equacions en derivades parcials, Differential equations, Hyperbolic, Classificació AMS::80 Classical thermodynamics, heat transfer::80A Thermodynamics and heat transfer, Heat and mass transfer, heat flow, Waves, three-phase-lag, heat transfer::80A Thermodynamics and heat transfer, relaxation parameters, Stability in context of PDEs, Stability, Hyperbolic models in heat conduction, Model
Differential equations, Àrees temàtiques de la UPC::Física::Termodinàmica, :35 Partial differential equations::35L Partial differential equations of hyperbolic type [Classificació AMS], :Matemàtiques i estadística::Equacions diferencials i integrals::Equacions en derivades parcials [Àrees temàtiques de la UPC], Termodinàmica -- Matemàtica, Classificació AMS::80 Classical thermodynamics, hyperbolic models in heat conduction, :Física::Termodinàmica [Àrees temàtiques de la UPC], Heat--Transmission--Mathematics, info:eu-repo/classification/ddc/510, Exponential Stability, Hyperbolic, Equacions diferencials hiperbòliques, Calor -- Transmissió -- Matemàtica, Classificació AMS::35 Partial differential equations::35L Partial differential equations of hyperbolic type, Qualitative aspects, Generalized thermoelasticity, :80 Classical thermodynamics, heat transfer::80A Thermodynamics and heat transfer [Classificació AMS], Asymptotic behavior of solutions to PDEs, dual-phase-lag, Thermodynamics--Mathematics, Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Equacions en derivades parcials, Differential equations, Hyperbolic, Classificació AMS::80 Classical thermodynamics, heat transfer::80A Thermodynamics and heat transfer, Heat and mass transfer, heat flow, Waves, three-phase-lag, heat transfer::80A Thermodynamics and heat transfer, relaxation parameters, Stability in context of PDEs, Stability, Hyperbolic models in heat conduction, Model
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