General Decay and Blowing-Up Solutions of a Nonlinear Wave Equation With Nonlocal in Time Damping and Infinite Memory

Mokhtar Kirane; Radhouane Aounallah; Lotfi Jlali

doi:10.1002/mma.10777

General Decay and Blowing-Up Solutions of a Nonlinear Wave Equation With Nonlocal in Time Damping and Infinite Memory

Mokhtar Kirane, Radhouane Aounallah, Lotfi Jlali

Mathematics

Imam Mohammad Ibn Saud Islamic University

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

3 Scopus citations

Abstract

This paper shows that long-term stability and blowing-up solutions for a nonlinear wave equation with a nonlocal damping of Choi and MacCamy type and a nonlocal dispersion can occur. The method of proof of general decay relies on a suitable Lyapunov functional. The method of proof of blow up in finite time of some solutions relies on the concavity method.

Original language	British English
Pages (from-to)	9046-9057
Number of pages	12
Journal	Mathematical Methods in the Applied Sciences
Volume	48
Issue number	8
DOIs	https://doi.org/10.1002/mma.10777
State	Published - 30 May 2025

Keywords

blowing-up solutions
general decay
global existence
nonlinear damping
wave equation

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10.1002/mma.10777

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title = "General Decay and Blowing-Up Solutions of a Nonlinear Wave Equation With Nonlocal in Time Damping and Infinite Memory",

abstract = "This paper shows that long-term stability and blowing-up solutions for a nonlinear wave equation with a nonlocal damping of Choi and MacCamy type and a nonlocal dispersion can occur. The method of proof of general decay relies on a suitable Lyapunov functional. The method of proof of blow up in finite time of some solutions relies on the concavity method.",

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AU - Kirane, Mokhtar

AU - Aounallah, Radhouane

AU - Jlali, Lotfi

PY - 2025/5/30

Y1 - 2025/5/30

N2 - This paper shows that long-term stability and blowing-up solutions for a nonlinear wave equation with a nonlocal damping of Choi and MacCamy type and a nonlocal dispersion can occur. The method of proof of general decay relies on a suitable Lyapunov functional. The method of proof of blow up in finite time of some solutions relies on the concavity method.

AB - This paper shows that long-term stability and blowing-up solutions for a nonlinear wave equation with a nonlocal damping of Choi and MacCamy type and a nonlocal dispersion can occur. The method of proof of general decay relies on a suitable Lyapunov functional. The method of proof of blow up in finite time of some solutions relies on the concavity method.

KW - blowing-up solutions

KW - general decay

KW - global existence

KW - nonlinear damping

KW - wave equation

UR - https://www.scopus.com/pages/publications/85217681581

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DO - 10.1002/mma.10777

M3 - Article

AN - SCOPUS:85217681581

SN - 0170-4214

VL - 48

SP - 9046

EP - 9057

JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

IS - 8

ER -

General Decay and Blowing-Up Solutions of a Nonlinear Wave Equation With Nonlocal in Time Damping and Infinite Memory

Abstract

Keywords

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