What question did this study set out to answer?

The study aims to explore the behavior of Kirchhoff-type wave equations with logarithmic sources and nonlocal damping.

April 15, 2026Journal of Inequalities and ApplicationsOpen Access

Asymptotic behavior study for a Kirchhoff-type system with nonlocal damping and logarithmic source terms

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Authors

AAAdel M. Al-MahdiKing Fahd University of Petroleum and Minerals MAMohammad M. Al-GharabliKing Fahd University of Petroleum and Minerals MKMohammad Kafini

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Implication

The investigation reports polynomial decay rates in a Kirchhoff-type system with nonlocal damping, indicating improvements in understanding its behavior.

Key Points

The study aims to explore the behavior of Kirchhoff-type wave equations with logarithmic sources and nonlocal damping.
Established local existence of weak solutions using the Faedo–Galerkin method.
Used the potential well-depth method for proving global well-posedness.
Applied Nakao’s lemma to derive decay rates for total energy.
Demonstrated global well-posedness for initial data in the stable set.
Derived a polynomial decay rate explicitly depending on nonlinear damping exponents.

Cite This Study

Al-Mahdi et al. (2026) studied this question.

synapsesocial.com/papers/69df2a99e4eeef8a2a6afa88 https://doi.org/10.1186/s13660-026-03475-y

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Implication

The investigation reports polynomial decay rates in a Kirchhoff-type system with nonlocal damping, indicating improvements in understanding its behavior.

Asymptotic behavior study for a Kirchhoff-type system with nonlocal damping and logarithmic source terms

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Member takes

Implication

Key Points

Cite This Study

Asymptotic behavior study for a Kirchhoff-type system with nonlocal damping and logarithmic source terms

Discussion

Member takes

Implication

Key Points

Cite This Study

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