### 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 τ_{q} and τ_{θ} are proposed. It is known that the system is exponentially stable if τ_{q} < 2τ_{θ} [22]. We here make two new contributions to this problem. First, we prove the polynomial stability in the case that τ_{q} = 2τ_{θ} 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 τ_{θ} is spatially dependent.

Language | English (US) |
---|---|

Pages | 177-190 |

Number of pages | 14 |

Journal | Communications on Pure and Applied Analysis |

Volume | 17 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2018 |

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### Keywords

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

### Cite this

*Communications on Pure and Applied Analysis*,

*17*(1), 177-190. https://doi.org/10.3934/cpaa.2018011

**Time decay in dual-phase-lag thermoelasticity : Critical case.** / Liu, Zhuangyi; Quintanilla, Ramón.

Research output: Contribution to journal › Article

*Communications on Pure and Applied Analysis*, vol. 17, no. 1, pp. 177-190. https://doi.org/10.3934/cpaa.2018011

}

TY - JOUR

T1 - Time decay in dual-phase-lag thermoelasticity

T2 - Communications on Pure and Applied Analysis

AU - Liu, Zhuangyi

AU - Quintanilla, Ramón

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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.

AB - 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.

KW - Exponential stability

KW - Phase-lag

KW - Polynomial stability

KW - Thermoelasticity

UR - http://www.scopus.com/inward/record.url?scp=85033775182&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85033775182&partnerID=8YFLogxK

U2 - 10.3934/cpaa.2018011

DO - 10.3934/cpaa.2018011

M3 - Article

VL - 17

SP - 177

EP - 190

JO - Communications on Pure and Applied Analysis

JF - Communications on Pure and Applied Analysis

SN - 1534-0392

IS - 1

ER -