Existence and Blow-up Study of a Quasilinear Wave Equation with Damping and Source Terms of Variable Exponents-type Acting on the Boundary

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

doi:10.1007/s10883-024-09695-z

Existence and Blow-up Study of a Quasilinear Wave Equation with Damping and Source Terms of Variable Exponents-type Acting on the Boundary

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

^*Corresponding author for this work

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

3 Scopus citations

Abstract

In this work, we are concerned with a quasilinear wave equation with nonlinear damping and source terms of variable exponents-type acting in a part of the boundary. Under suitable conditions on the exponents and the initial data, we study the blow-up properties. Firstly, by using Faedo-Galerkin method and Banach-Fixed-Point Theorem, we establish the existence of a weak solution, under suitable assumptions on the variable exponents and the initial data. Secondly, we show a finite time blow-up with lower and upper bound as well. Next, an infinite time blow-up is proved under some conditions in the exponents and the initial data.

Original language	English
Pages (from-to)	1-21
Number of pages	21
Journal	Journal of Dynamical and Control Systems
Volume	30
Issue number	2
DOIs	https://doi.org/10.1007/s10883-024-09695-z
State	Published - Jun 2024

Bibliographical note

Publisher Copyright:
© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.

Keywords

Blow-up
Faedo-Galerkin method and Banach-Fixed-Point Theorem
Quasilinear wave equation
Variable exponent

ASJC Scopus subject areas

Control and Systems Engineering
Algebra and Number Theory
Numerical Analysis
Control and Optimization

Access to Document

10.1007/s10883-024-09695-z

Cite this

@article{bcd847d0b9d04a1cb796fd49d567b69b,

title = "Existence and Blow-up Study of a Quasilinear Wave Equation with Damping and Source Terms of Variable Exponents-type Acting on the Boundary",

abstract = "In this work, we are concerned with a quasilinear wave equation with nonlinear damping and source terms of variable exponents-type acting in a part of the boundary. Under suitable conditions on the exponents and the initial data, we study the blow-up properties. Firstly, by using Faedo-Galerkin method and Banach-Fixed-Point Theorem, we establish the existence of a weak solution, under suitable assumptions on the variable exponents and the initial data. Secondly, we show a finite time blow-up with lower and upper bound as well. Next, an infinite time blow-up is proved under some conditions in the exponents and the initial data.",

keywords = "Blow-up, Faedo-Galerkin method and Banach-Fixed-Point Theorem, Quasilinear wave equation, Variable exponent",

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

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.",

year = "2024",

month = jun,

doi = "10.1007/s10883-024-09695-z",

language = "English",

volume = "30",

pages = "1--21",

journal = "Journal of Dynamical and Control Systems",

issn = "1079-2724",

publisher = "Springer New York",

number = "2",

}

TY - JOUR

T1 - Existence and Blow-up Study of a Quasilinear Wave Equation with Damping and Source Terms of Variable Exponents-type Acting on the Boundary

AU - Kafini, Mohammad

AU - Al-Gharabli, Mohammad M.

AU - Al-Mahdi, Adel M.

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.

PY - 2024/6

Y1 - 2024/6

N2 - In this work, we are concerned with a quasilinear wave equation with nonlinear damping and source terms of variable exponents-type acting in a part of the boundary. Under suitable conditions on the exponents and the initial data, we study the blow-up properties. Firstly, by using Faedo-Galerkin method and Banach-Fixed-Point Theorem, we establish the existence of a weak solution, under suitable assumptions on the variable exponents and the initial data. Secondly, we show a finite time blow-up with lower and upper bound as well. Next, an infinite time blow-up is proved under some conditions in the exponents and the initial data.

AB - In this work, we are concerned with a quasilinear wave equation with nonlinear damping and source terms of variable exponents-type acting in a part of the boundary. Under suitable conditions on the exponents and the initial data, we study the blow-up properties. Firstly, by using Faedo-Galerkin method and Banach-Fixed-Point Theorem, we establish the existence of a weak solution, under suitable assumptions on the variable exponents and the initial data. Secondly, we show a finite time blow-up with lower and upper bound as well. Next, an infinite time blow-up is proved under some conditions in the exponents and the initial data.

KW - Blow-up

KW - Faedo-Galerkin method and Banach-Fixed-Point Theorem

KW - Quasilinear wave equation

KW - Variable exponent

UR - https://www.scopus.com/pages/publications/85192884821

U2 - 10.1007/s10883-024-09695-z

DO - 10.1007/s10883-024-09695-z

M3 - Article

AN - SCOPUS:85192884821

SN - 1079-2724

VL - 30

SP - 1

EP - 21

JO - Journal of Dynamical and Control Systems

JF - Journal of Dynamical and Control Systems

IS - 2

ER -

Existence and Blow-up Study of a Quasilinear Wave Equation with Damping and Source Terms of Variable Exponents-type Acting on the Boundary

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Fingerprint

Cite this