General Decay Estimate for a Weakly Dissipative Viscoelastic Suspension Bridge

Salim A. Messaoudi; Soh Edwin Mukiawa; Mohammad M. Al-Gharabli

doi:10.1007/978-3-031-41420-6_2

General Decay Estimate for a Weakly Dissipative Viscoelastic Suspension Bridge

Salim A. Messaoudi
, Soh Edwin Mukiawa
, Mohammad M. Al-Gharabli^*

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

In this article, we investigate the following weakly dissipative plate equation: u_tt(x,y,t)+Δ²u(x,y,t)+∫₀^tg(t−s)u_xx(x,y,s)ds−u_xxt=0,Ω×(0,T). Under some mild conditions on the relaxation function g, we show that the solution energy has general decay estimate. We also give some examples to illustrate our result. The multiplier method, the properties of the convex and the dual of the convex functions, Jensen’s inequality and the generalized Young inequality are used to establish the stability results.

Original language	English
Title of host publication	Trends in Mathematics
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	15-26
Number of pages	12
DOIs	https://doi.org/10.1007/978-3-031-41420-6_2
State	Published - 2024

Publication series

Name	Trends in Mathematics
Volume	Part F2357
ISSN (Print)	2297-0215
ISSN (Electronic)	2297-024X

Bibliographical note

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

Keywords

35B40
74F05
93C20
93D15
93D20
Decay
Partially hinged
Plate equation
Suspension bridge
Viscoelastic

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1007/978-3-031-41420-6_2

Cite this

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title = "General Decay Estimate for a Weakly Dissipative Viscoelastic Suspension Bridge",

abstract = "In this article, we investigate the following weakly dissipative plate equation: utt(x,y,t)+Δ2u(x,y,t)+∫0tg(t−s)uxx(x,y,s)ds−uxxt=0,Ω×(0,T). Under some mild conditions on the relaxation function g, we show that the solution energy has general decay estimate. We also give some examples to illustrate our result. The multiplier method, the properties of the convex and the dual of the convex functions, Jensen{\textquoteright}s inequality and the generalized Young inequality are used to establish the stability results.",

keywords = "35B40, 74F05, 93C20, 93D15, 93D20, Decay, Partially hinged, Plate equation, Suspension bridge, Viscoelastic",

author = "Messaoudi, \{Salim A.\} and Mukiawa, \{Soh Edwin\} and Al-Gharabli, \{Mohammad M.\}",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.",

year = "2024",

doi = "10.1007/978-3-031-41420-6\_2",

language = "English",

series = "Trends in Mathematics",

publisher = "Springer Science and Business Media Deutschland GmbH",

pages = "15--26",

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}

General Decay Estimate for a Weakly Dissipative Viscoelastic Suspension Bridge. / Messaoudi, Salim A.; Mukiawa, Soh Edwin; Al-Gharabli, Mohammad M.
Trends in Mathematics. Springer Science and Business Media Deutschland GmbH, 2024. p. 15-26 (Trends in Mathematics; Vol. Part F2357).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

TY - CHAP

T1 - General Decay Estimate for a Weakly Dissipative Viscoelastic Suspension Bridge

AU - Messaoudi, Salim A.

AU - Mukiawa, Soh Edwin

AU - Al-Gharabli, Mohammad M.

N1 - Publisher Copyright: © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.

PY - 2024

Y1 - 2024

N2 - In this article, we investigate the following weakly dissipative plate equation: utt(x,y,t)+Δ2u(x,y,t)+∫0tg(t−s)uxx(x,y,s)ds−uxxt=0,Ω×(0,T). Under some mild conditions on the relaxation function g, we show that the solution energy has general decay estimate. We also give some examples to illustrate our result. The multiplier method, the properties of the convex and the dual of the convex functions, Jensen’s inequality and the generalized Young inequality are used to establish the stability results.

AB - In this article, we investigate the following weakly dissipative plate equation: utt(x,y,t)+Δ2u(x,y,t)+∫0tg(t−s)uxx(x,y,s)ds−uxxt=0,Ω×(0,T). Under some mild conditions on the relaxation function g, we show that the solution energy has general decay estimate. We also give some examples to illustrate our result. The multiplier method, the properties of the convex and the dual of the convex functions, Jensen’s inequality and the generalized Young inequality are used to establish the stability results.

KW - 35B40

KW - 74F05

KW - 93C20

KW - 93D15

KW - 93D20

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KW - Partially hinged

KW - Plate equation

KW - Suspension bridge

KW - Viscoelastic

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AN - SCOPUS:85187195132

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SP - 15

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BT - Trends in Mathematics

PB - Springer Science and Business Media Deutschland GmbH

ER -

General Decay Estimate for a Weakly Dissipative Viscoelastic Suspension Bridge

Abstract

Publication series

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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Cite this