Existence and stability results of a plate equation with nonlinear damping and source term

Mohammad M. Al-Gharabli; Adel M. Al-Mahdi

doi:10.3934/ERA.2022205

Existence and stability results of a plate equation with nonlinear damping and source term

Mohammad M. Al-Gharabli
, Adel M. Al-Mahdi^*

^*Corresponding author for this work

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

6 Scopus citations

Abstract

The main goal of this work is to investigate the following nonlinear plate equation [Formula Presented], which models suspension bridges. Firstly, we prove the local existence using Faedo-Galerkin method and Banach fixed point theorem. Secondly, we prove the global existence by using the well-depth method. Finally, we establish explicit and general decay results for the energy of solutions of the problem. Our decay results depend on the functions α and g and obtained without any restriction growth assumption on g at the origin. The multiplier method, properties of the convex functions, Jensen’s inequality and the generalized Young inequality are used to establish the stability results.

Original language	English
Pages (from-to)	4038-4065
Number of pages	28
Journal	Electronic Research Archive
Volume	30
Issue number	11
DOIs	https://doi.org/10.3934/ERA.2022205
State	Published - 2022

Bibliographical note

Publisher Copyright:
© 2022 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)

Keywords

Banach fixed point theorem
Galerkin method
General decay
Nonlinear frictional damping
Plate equation

ASJC Scopus subject areas

General Mathematics

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10.3934/ERA.2022205

Cite this

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title = "Existence and stability results of a plate equation with nonlinear damping and source term",

abstract = "The main goal of this work is to investigate the following nonlinear plate equation [Formula Presented], which models suspension bridges. Firstly, we prove the local existence using Faedo-Galerkin method and Banach fixed point theorem. Secondly, we prove the global existence by using the well-depth method. Finally, we establish explicit and general decay results for the energy of solutions of the problem. Our decay results depend on the functions α and g and obtained without any restriction growth assumption on g at the origin. The multiplier method, properties of the convex functions, Jensen{\textquoteright}s inequality and the generalized Young inequality are used to establish the stability results.",

keywords = "Banach fixed point theorem, Galerkin method, General decay, Nonlinear frictional damping, Plate equation",

author = "Al-Gharabli, \{Mohammad M.\} and Al-Mahdi, \{Adel M.\}",

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year = "2022",

doi = "10.3934/ERA.2022205",

language = "English",

volume = "30",

pages = "4038--4065",

journal = "Electronic Research Archive",

issn = "1935-9179",

publisher = "American Mathematical Society",

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T1 - Existence and stability results of a plate equation with nonlinear damping and source term

AU - Al-Gharabli, Mohammad M.

AU - Al-Mahdi, Adel M.

N1 - Publisher Copyright: © 2022 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)

PY - 2022

Y1 - 2022

N2 - The main goal of this work is to investigate the following nonlinear plate equation [Formula Presented], which models suspension bridges. Firstly, we prove the local existence using Faedo-Galerkin method and Banach fixed point theorem. Secondly, we prove the global existence by using the well-depth method. Finally, we establish explicit and general decay results for the energy of solutions of the problem. Our decay results depend on the functions α and g and obtained without any restriction growth assumption on g at the origin. The multiplier method, properties of the convex functions, Jensen’s inequality and the generalized Young inequality are used to establish the stability results.

AB - The main goal of this work is to investigate the following nonlinear plate equation [Formula Presented], which models suspension bridges. Firstly, we prove the local existence using Faedo-Galerkin method and Banach fixed point theorem. Secondly, we prove the global existence by using the well-depth method. Finally, we establish explicit and general decay results for the energy of solutions of the problem. Our decay results depend on the functions α and g and obtained without any restriction growth assumption on g at the origin. The multiplier method, properties of the convex functions, Jensen’s inequality and the generalized Young inequality are used to establish the stability results.

KW - Banach fixed point theorem

KW - Galerkin method

KW - General decay

KW - Nonlinear frictional damping

KW - Plate equation

UR - https://www.scopus.com/pages/publications/85145903620

U2 - 10.3934/ERA.2022205

DO - 10.3934/ERA.2022205

M3 - Article

AN - SCOPUS:85145903620

SN - 1935-9179

VL - 30

SP - 4038

EP - 4065

JO - Electronic Research Archive

JF - Electronic Research Archive

IS - 11

ER -

Existence and stability results of a plate equation with nonlinear damping and source term

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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