Existence and blow up time estimate for a nonlinear Cauchy problem with variable exponents: theory and numerics

Mohammad Kafini; Jamilu Hashim Hassan; Adel M. Al-Mahdi; Jamal H. Al-Smail

doi:10.1080/00207160.2023.2176196

Existence and blow up time estimate for a nonlinear Cauchy problem with variable exponents: theory and numerics

Mohammad Kafini, Jamilu Hashim Hassan, Adel M. Al-Mahdi^*, Jamal H. Al-Smail

^*Corresponding author for this work

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

Abstract

A nonlinear Cauchy problem of a wave equation with variable exponents is considered. The damping term is subjected to a coefficient of both variables space and time. We prove the local existence of solutions using the Galerkin approach while the blow-up result is obtained via the perturbed energy method. We finally end our paper with some numerical illustrations. Problems that are frequently used in the literature are special cases.

Original language	English
Pages (from-to)	1228-1247
Number of pages	20
Journal	International Journal of Computer Mathematics
Volume	100
Issue number	6
DOIs	https://doi.org/10.1080/00207160.2023.2176196
State	Published - 2023

Bibliographical note

Funding Information:
The authors would like to express their sincere thanks to King Fahd University of Petroleum and Minerals. The authors also thank the referees for their very careful reading and valuable comments. This work was funded by KFUPM under Project No. # SB201026.

Publisher Copyright:
© 2023 Informa UK Limited, trading as Taylor & Francis Group.

Keywords

35A01
35B45
35L15
35L70
65M60
Blow-up
finite time
local existence
numerical computations
variable exponents

ASJC Scopus subject areas

Computer Science Applications
Computational Theory and Mathematics
Applied Mathematics

Access to Document

10.1080/00207160.2023.2176196

Cite this

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title = "Existence and blow up time estimate for a nonlinear Cauchy problem with variable exponents: theory and numerics",

abstract = "A nonlinear Cauchy problem of a wave equation with variable exponents is considered. The damping term is subjected to a coefficient of both variables space and time. We prove the local existence of solutions using the Galerkin approach while the blow-up result is obtained via the perturbed energy method. We finally end our paper with some numerical illustrations. Problems that are frequently used in the literature are special cases.",

keywords = "35A01, 35B45, 35L15, 35L70, 65M60, Blow-up, finite time, local existence, numerical computations, variable exponents",

author = "Mohammad Kafini and Hassan, {Jamilu Hashim} and Al-Mahdi, {Adel M.} and Al-Smail, {Jamal H.}",

note = "Funding Information: The authors would like to express their sincere thanks to King Fahd University of Petroleum and Minerals. The authors also thank the referees for their very careful reading and valuable comments. This work was funded by KFUPM under Project No. # SB201026. Publisher Copyright: {\textcopyright} 2023 Informa UK Limited, trading as Taylor & Francis Group.",

year = "2023",

doi = "10.1080/00207160.2023.2176196",

language = "English",

volume = "100",

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journal = "International Journal of Computer Mathematics",

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T2 - theory and numerics

AU - Kafini, Mohammad

AU - Hassan, Jamilu Hashim

AU - Al-Mahdi, Adel M.

AU - Al-Smail, Jamal H.

N1 - Funding Information: The authors would like to express their sincere thanks to King Fahd University of Petroleum and Minerals. The authors also thank the referees for their very careful reading and valuable comments. This work was funded by KFUPM under Project No. # SB201026. Publisher Copyright: © 2023 Informa UK Limited, trading as Taylor & Francis Group.

PY - 2023

Y1 - 2023

N2 - A nonlinear Cauchy problem of a wave equation with variable exponents is considered. The damping term is subjected to a coefficient of both variables space and time. We prove the local existence of solutions using the Galerkin approach while the blow-up result is obtained via the perturbed energy method. We finally end our paper with some numerical illustrations. Problems that are frequently used in the literature are special cases.

AB - A nonlinear Cauchy problem of a wave equation with variable exponents is considered. The damping term is subjected to a coefficient of both variables space and time. We prove the local existence of solutions using the Galerkin approach while the blow-up result is obtained via the perturbed energy method. We finally end our paper with some numerical illustrations. Problems that are frequently used in the literature are special cases.

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KW - 35B45

KW - 35L15

KW - 35L70

KW - 65M60

KW - Blow-up

KW - finite time

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KW - numerical computations

KW - variable exponents

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JO - International Journal of Computer Mathematics

JF - International Journal of Computer Mathematics

IS - 6

ER -

Existence and blow up time estimate for a nonlinear Cauchy problem with variable exponents: theory and numerics

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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