### Abstract

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 R^{n} with smooth boundary. We obtain analyticity for the associated C_{0}−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 λ_{1} is the smallest eigenvalue of the negative Laplacian on Ω with Dirichlet boundary condition.

Original language | English (US) |
---|---|

Article number | 106038 |

Journal | Applied Mathematics Letters |

Volume | 100 |

DOIs | |

State | Published - Feb 1 2020 |

### Fingerprint

### Keywords

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

### Cite this

*Applied Mathematics Letters*,

*100*, [106038]. https://doi.org/10.1016/j.aml.2019.106038

**On the regularity and stability of the dual-phase-lag equation.** / Liu, Zhuangyi; Quintanilla, Ramon; Wang, Yang.

Research output: Contribution to journal › Article

*Applied Mathematics Letters*, vol. 100, 106038. https://doi.org/10.1016/j.aml.2019.106038

}

TY - JOUR

T1 - On the regularity and stability of the dual-phase-lag equation

AU - Liu, Zhuangyi

AU - Quintanilla, Ramon

AU - Wang, Yang

PY - 2020/2/1

Y1 - 2020/2/1

N2 - 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.

AB - 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.

KW - Analyticity

KW - Dual-phase-lag heat equation

KW - Exponential stability

UR - http://www.scopus.com/inward/record.url?scp=85072284784&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85072284784&partnerID=8YFLogxK

U2 - 10.1016/j.aml.2019.106038

DO - 10.1016/j.aml.2019.106038

M3 - Article

VL - 100

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

SN - 0893-9659

M1 - 106038

ER -