Time decay in dual-phase-lag thermoelasticity: Critical case

Zhuangyi Liu, Ramón Quintanilla

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9 Scopus citations

Abstract

This note is devoted to the study of the time decay of the onedimensional dual-phase-lag thermoelasticity. In this theory two delay parameters τq and τθ are proposed. It is known that the system is exponentially stable if τq < 2τθ [22]. We here make two new contributions to this problem. First, we prove the polynomial stability in the case that τq = 2τθ as well the optimality of this decay rate. Second, we prove that the exponential stability remains true even if the inequality only holds in a proper sub-interval of the spatial domain, when τθ is spatially dependent.

Original languageEnglish (US)
Pages (from-to)177-190
Number of pages14
JournalCommunications on Pure and Applied Analysis
Volume17
Issue number1
DOIs
StatePublished - Jan 2018

Bibliographical note

Funding Information:
2000 Mathematics Subject Classification. Primary: 35Q70, 35B40; Secondary: 74F05. Key words and phrases. Phase-lag, thermoelasticity, polynomial stability, exponential stability. The second author R. Q. is supported by the Projects “Análisis Matemático de las Ecuaciones en Derivada Parciales de la Termomecánica“(MTM2013-42004-P), “Análisis Matemático de Pro-blemas de la Termomecánica“(MTM2016-74934-P), (AEI/FEDER, UE) of the Spanish Ministry of Economy and Competitiveness. ∗ Corresponding author: Ramón Quintanilla.

Keywords

  • Exponential stability
  • Phase-lag
  • Polynomial stability
  • Thermoelasticity

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