GROWTH AND BLOW-UP OF VISCOELASTIC WAVE EQUATION SOLUTIONS WITH LOGARITHMIC SOURCE, ACOUSTIC AND FRACTIONAL CONDITIONS, AND NONLINEAR BOUNDARY DELAY

Abdelbaki Choucha; Mohamed Haiour; Rashid Jan; Mohammad Shahrouzi; Praveen Agarwal; Mohamed Abdalla

doi:10.3934/dcdss.2025009

GROWTH AND BLOW-UP OF VISCOELASTIC WAVE EQUATION SOLUTIONS WITH LOGARITHMIC SOURCE, ACOUSTIC AND FRACTIONAL CONDITIONS, AND NONLINEAR BOUNDARY DELAY

Abdelbaki Choucha
, Mohamed Haiour
, Rashid Jan
, Mohammad Shahrouzi
, Praveen Agarwal
, Mohamed Abdalla

Nonlinear Dynamic Research Centre (NDRC)

University of Laghouat
Ghardaia University
Badji Mokhtar University
Universiti Tenaga Nasional
Near East University
Ferdowsi University of Mashhad
International College of Engineering
King Khalid University

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

3 Scopus citations

Abstract

This study focuses on a nonlinear viscoelastic wave equation involving logarithmic nonlinearity. It considers a nonlinear distributed delay influencing the boundary feedback, which is coupled with acoustic and fractional boundary conditions. Following the proof of global existence, we demonstrate the exponential growth and blow-up of solutions with positive initial energy under appropriate assumptions and for a general case of the kernel. This finding broadens and enhances earlier results.

Original language	English
Pages (from-to)	60-80
Number of pages	21
Journal	Discrete and Continuous Dynamical Systems - Series S
Volume	23
DOIs	https://doi.org/10.3934/dcdss.2025009
State	Published - 12 Mar 2026

Keywords

Fractional damping
blow up
distributed delay
exponential growth
logarithmic nonlinearity
viscoelasticity

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10.3934/dcdss.2025009

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title = "GROWTH AND BLOW-UP OF VISCOELASTIC WAVE EQUATION SOLUTIONS WITH LOGARITHMIC SOURCE, ACOUSTIC AND FRACTIONAL CONDITIONS, AND NONLINEAR BOUNDARY DELAY",

abstract = "This study focuses on a nonlinear viscoelastic wave equation involving logarithmic nonlinearity. It considers a nonlinear distributed delay influencing the boundary feedback, which is coupled with acoustic and fractional boundary conditions. Following the proof of global existence, we demonstrate the exponential growth and blow-up of solutions with positive initial energy under appropriate assumptions and for a general case of the kernel. This finding broadens and enhances earlier results.",

keywords = "Fractional damping, blow up, distributed delay, exponential growth, logarithmic nonlinearity, viscoelasticity",

author = "Abdelbaki Choucha and Mohamed Haiour and Rashid Jan and Mohammad Shahrouzi and Praveen Agarwal and Mohamed Abdalla",

year = "2026",

month = mar,

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doi = "10.3934/dcdss.2025009",

language = "English",

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T1 - GROWTH AND BLOW-UP OF VISCOELASTIC WAVE EQUATION SOLUTIONS WITH LOGARITHMIC SOURCE, ACOUSTIC AND FRACTIONAL CONDITIONS, AND NONLINEAR BOUNDARY DELAY

AU - Choucha, Abdelbaki

AU - Haiour, Mohamed

AU - Jan, Rashid

AU - Shahrouzi, Mohammad

AU - Agarwal, Praveen

AU - Abdalla, Mohamed

PY - 2026/3/12

Y1 - 2026/3/12

N2 - This study focuses on a nonlinear viscoelastic wave equation involving logarithmic nonlinearity. It considers a nonlinear distributed delay influencing the boundary feedback, which is coupled with acoustic and fractional boundary conditions. Following the proof of global existence, we demonstrate the exponential growth and blow-up of solutions with positive initial energy under appropriate assumptions and for a general case of the kernel. This finding broadens and enhances earlier results.

AB - This study focuses on a nonlinear viscoelastic wave equation involving logarithmic nonlinearity. It considers a nonlinear distributed delay influencing the boundary feedback, which is coupled with acoustic and fractional boundary conditions. Following the proof of global existence, we demonstrate the exponential growth and blow-up of solutions with positive initial energy under appropriate assumptions and for a general case of the kernel. This finding broadens and enhances earlier results.

KW - Fractional damping

KW - blow up

KW - distributed delay

KW - exponential growth

KW - logarithmic nonlinearity

KW - viscoelasticity

UR - https://www.scopus.com/pages/publications/105033622929

U2 - 10.3934/dcdss.2025009

DO - 10.3934/dcdss.2025009

M3 - Article

AN - SCOPUS:105033622929

SN - 1937-1632

VL - 23

SP - 60

EP - 80

JO - Discrete and Continuous Dynamical Systems - Series S

JF - Discrete and Continuous Dynamical Systems - Series S

ER -

GROWTH AND BLOW-UP OF VISCOELASTIC WAVE EQUATION SOLUTIONS WITH LOGARITHMIC SOURCE, ACOUSTIC AND FRACTIONAL CONDITIONS, AND NONLINEAR BOUNDARY DELAY

Abstract

Keywords

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