Asymptotic Analysis of Solutions for a p-Kirchhoff Type Hyperbolic Equation with Dynamic Boundary Conditions

Billel Gheraibia; Nouri Boumaza; Adel M. Al-Mahdi; Mohammad M. Al-Gharabli

doi:10.1007/s00009-025-02934-y

Asymptotic Analysis of Solutions for a p-Kirchhoff Type Hyperbolic Equation with Dynamic Boundary Conditions

Billel Gheraibia
, Nouri Boumaza
, Adel M. Al-Mahdi^*
, Mohammad M. Al-Gharabli

^*Corresponding author for this work

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

1 Scopus citations

Abstract

The aim of this study is to analyze the global existence, general decay, and blow-up behavior of solutions for a class of p-Kirchhoff-type hyperbolic equations with damping terms and dynamic boundary conditions. The global existence of solutions is demonstrated using potential well theory, while the general decay of energy—encompassing exponential and polynomial decay as particular cases—is established through multiplier techniques combined with nonlinear integral inequalities. Finally, the blow-up of solutions is proven in the case of negative initial energy.

Original language	English
Article number	164
Journal	Mediterranean Journal of Mathematics
Volume	22
Issue number	6
DOIs	https://doi.org/10.1007/s00009-025-02934-y
State	Published - Sep 2025

Bibliographical note

Publisher Copyright:
© The Author(s), under exclusive licence to Springer Nature Switzerland AG 2025.

Keywords

blow-up
decay rate
dynamic boundary conditions
global existence
p-Kirchhoff type equation

ASJC Scopus subject areas

General Mathematics

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10.1007/s00009-025-02934-y

Cite this

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title = "Asymptotic Analysis of Solutions for a p-Kirchhoff Type Hyperbolic Equation with Dynamic Boundary Conditions",

abstract = "The aim of this study is to analyze the global existence, general decay, and blow-up behavior of solutions for a class of p-Kirchhoff-type hyperbolic equations with damping terms and dynamic boundary conditions. The global existence of solutions is demonstrated using potential well theory, while the general decay of energy—encompassing exponential and polynomial decay as particular cases—is established through multiplier techniques combined with nonlinear integral inequalities. Finally, the blow-up of solutions is proven in the case of negative initial energy.",

keywords = "blow-up, decay rate, dynamic boundary conditions, global existence, p-Kirchhoff type equation",

author = "Billel Gheraibia and Nouri Boumaza and Al-Mahdi, \{Adel M.\} and Al-Gharabli, \{Mohammad M.\}",

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AU - Gheraibia, Billel

AU - Boumaza, Nouri

AU - Al-Mahdi, Adel M.

AU - Al-Gharabli, Mohammad M.

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2025.

PY - 2025/9

Y1 - 2025/9

N2 - The aim of this study is to analyze the global existence, general decay, and blow-up behavior of solutions for a class of p-Kirchhoff-type hyperbolic equations with damping terms and dynamic boundary conditions. The global existence of solutions is demonstrated using potential well theory, while the general decay of energy—encompassing exponential and polynomial decay as particular cases—is established through multiplier techniques combined with nonlinear integral inequalities. Finally, the blow-up of solutions is proven in the case of negative initial energy.

AB - The aim of this study is to analyze the global existence, general decay, and blow-up behavior of solutions for a class of p-Kirchhoff-type hyperbolic equations with damping terms and dynamic boundary conditions. The global existence of solutions is demonstrated using potential well theory, while the general decay of energy—encompassing exponential and polynomial decay as particular cases—is established through multiplier techniques combined with nonlinear integral inequalities. Finally, the blow-up of solutions is proven in the case of negative initial energy.

KW - blow-up

KW - decay rate

KW - dynamic boundary conditions

KW - global existence

KW - p-Kirchhoff type equation

UR - https://www.scopus.com/pages/publications/105013456879

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DO - 10.1007/s00009-025-02934-y

M3 - Article

AN - SCOPUS:105013456879

SN - 1660-5446

VL - 22

JO - Mediterranean Journal of Mathematics

JF - Mediterranean Journal of Mathematics

IS - 6

M1 - 164

ER -

Asymptotic Analysis of Solutions for a p-Kirchhoff Type Hyperbolic Equation with Dynamic Boundary Conditions

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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