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

2 Scopus citations

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

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

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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 = "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",

issn = "0020-7160",

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T1 - Existence and blow up time estimate for a nonlinear Cauchy problem with variable exponents

T2 - theory and numerics

AU - Kafini, Mohammad

AU - Hassan, Jamilu Hashim

AU - Al-Mahdi, Adel M.

AU - Al-Smail, Jamal H.

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.

KW - 35A01

KW - 35B45

KW - 35L15

KW - 35L70

KW - 65M60

KW - Blow-up

KW - finite time

KW - local existence

KW - numerical computations

KW - variable exponents

UR - https://www.scopus.com/pages/publications/85148203850

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DO - 10.1080/00207160.2023.2176196

M3 - Article

AN - SCOPUS:85148203850

SN - 0020-7160

VL - 100

SP - 1228

EP - 1247

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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