A new approach to abstract linear viscoelastic equation in Hilbert space

Jian Hua Chen; Wen Ying Lu

doi:10.1007/s00033-023-02159-7

A new approach to abstract linear viscoelastic equation in Hilbert space

Jian Hua Chen^*, Wen Ying Lu

^*Corresponding author for this work

Research output: Contribution to journal › Journal Article › peer-review

1 Citation (Scopus)

Abstract

We study an abstract linear viscoelastic equation in Hilbert space. It fits some convolution type of integro-differential equations which govern dynamics in viscoelastic or thermoviscoelastic materials. A new semigroup approach is proposed which is adapted from a semigroup approach designed originally to a second-order abstract linear integro-differential equation. As compared with the existing semigroup approach, the system contraction can be obtained readily. Sufficient conditions for the system exponential stability are also established. An illustrative example is given, and numerical simulations are provided. They are in good agreement with the theoretical analysis.

Original language	English
Article number	13
Journal	Zeitschrift fur Angewandte Mathematik und Physik
Volume	75
Issue number	1
DOIs	https://doi.org/10.1007/s00033-023-02159-7
Publication status	Published - Feb 2024
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2024, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

Keywords

Exponential stability
Memory kernel
Operator semigroup
Viscoelastic equation

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10.1007/s00033-023-02159-7

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abstract = "We study an abstract linear viscoelastic equation in Hilbert space. It fits some convolution type of integro-differential equations which govern dynamics in viscoelastic or thermoviscoelastic materials. A new semigroup approach is proposed which is adapted from a semigroup approach designed originally to a second-order abstract linear integro-differential equation. As compared with the existing semigroup approach, the system contraction can be obtained readily. Sufficient conditions for the system exponential stability are also established. An illustrative example is given, and numerical simulations are provided. They are in good agreement with the theoretical analysis.",

keywords = "Exponential stability, Memory kernel, Operator semigroup, Viscoelastic equation",

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T1 - A new approach to abstract linear viscoelastic equation in Hilbert space

AU - Chen, Jian Hua

AU - Lu, Wen Ying

PY - 2024/2

Y1 - 2024/2

N2 - We study an abstract linear viscoelastic equation in Hilbert space. It fits some convolution type of integro-differential equations which govern dynamics in viscoelastic or thermoviscoelastic materials. A new semigroup approach is proposed which is adapted from a semigroup approach designed originally to a second-order abstract linear integro-differential equation. As compared with the existing semigroup approach, the system contraction can be obtained readily. Sufficient conditions for the system exponential stability are also established. An illustrative example is given, and numerical simulations are provided. They are in good agreement with the theoretical analysis.

AB - We study an abstract linear viscoelastic equation in Hilbert space. It fits some convolution type of integro-differential equations which govern dynamics in viscoelastic or thermoviscoelastic materials. A new semigroup approach is proposed which is adapted from a semigroup approach designed originally to a second-order abstract linear integro-differential equation. As compared with the existing semigroup approach, the system contraction can be obtained readily. Sufficient conditions for the system exponential stability are also established. An illustrative example is given, and numerical simulations are provided. They are in good agreement with the theoretical analysis.

KW - Exponential stability

KW - Memory kernel

KW - Operator semigroup

KW - Viscoelastic equation

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DO - 10.1007/s00033-023-02159-7

M3 - Journal Article

AN - SCOPUS:85182177139

SN - 0044-2275

VL - 75

JO - Zeitschrift fur Angewandte Mathematik und Physik

JF - Zeitschrift fur Angewandte Mathematik und Physik

IS - 1

M1 - 13

ER -

A new approach to abstract linear viscoelastic equation in Hilbert space

Abstract

Bibliographical note

Keywords

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