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

Zhuangyi Liu, Ramon Quintanilla, Yang Wang

Research output: Contribution to journalArticle

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 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
Volume100
DOIs
StatePublished - Feb 1 2020

Fingerprint

Phase-lag
Asymptotic stability
Spectrum analysis
Partial differential equations
Regularity
Boundary conditions
Spectrum Analysis
Smallest Eigenvalue
Linear partial differential equation
Analyticity
Exponential Stability
Heat Equation
Dirichlet Boundary Conditions
Bounded Domain
Approximation
Hot Temperature

Keywords

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

Cite this

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

In: Applied Mathematics Letters, Vol. 100, 106038, 01.02.2020.

Research output: Contribution to journalArticle

Liu, Zhuangyi ; Quintanilla, Ramon ; Wang, Yang. / On the regularity and stability of the dual-phase-lag equation. In: Applied Mathematics Letters. 2020 ; Vol. 100.
@article{be40e31f132b49748614aba80f4f30c6,
title = "On the regularity and stability of the dual-phase-lag equation",
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 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.",
keywords = "Analyticity, Dual-phase-lag heat equation, Exponential stability",
author = "Zhuangyi Liu and Ramon Quintanilla and Yang Wang",
year = "2020",
month = "2",
day = "1",
doi = "10.1016/j.aml.2019.106038",
language = "English (US)",
volume = "100",
journal = "Applied Mathematics Letters",
issn = "0893-9659",
publisher = "Elsevier Limited",

}

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 -