On the regularity and stability of the dual-phase-lag equation

Zhuangyi Liu, Ramon Quintanilla, Yang Wang

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In this paper we consider the following linear partial differential equation which is usually seen as an approximation to the dual-phase-lag heat equation proposed by Tzou. [Formula presented] on a bounded domain Ω in Rn with smooth boundary. We obtain analyticity for the associated C0−semigroup. Moreover, we also obtain exponential stability of the solutions by spectrum analysis and Hurwitz criterion under one of the following conditions: (i). [Formula presented] (ii). [Formula presented] where λ1 is the smallest eigenvalue of the negative Laplacian on Ω with Dirichlet boundary condition.

Original languageEnglish (US)
Article number106038
JournalApplied Mathematics Letters
StatePublished - Feb 2020

Bibliographical note

Funding Information:
R. Q. is supported by the Project “Análisis Matemático de Problemas de la Termomecánica“ ( MTM2016-74934-P ) (AEI/FEDER, UE) of the Spanish Ministry of Economy and Competitiveness .


  • Analyticity
  • Dual-phase-lag heat equation
  • Exponential stability

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