Work

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

Year: 2026

Type: article

Abstract: This paper investigates a system of coupled Kirchhoff-type wave equations with logarithmic source terms and nonlinear nonlocal damping. The local existence of weak solutions is established via the Faedo–Galerkin method, while the potential well-depth method is employed to prove the global well-posedness of the initial–boundary value problem for initial data in the stable set. Furthermore, applying Nakao’s lemma to the energy identity, we derive a polynomial decay rate for the system total energy, with the decay rate explicitly depending on the nonlinear damping exponents. These results extend previous works on Kirchhoff-type systems by addressing logarithmic nonlinearities in the presence of nonlinear nonlocal dissipation.

Source: Journal of Inequalities and Applications

DOI: 10.1186/s13660-026-03475-y

Authors: Adel M. Al-Mahdi, Mohammad M. Al-Gharabli, Mohammad Kafini

Institution: King Fahd University of Petroleum and Minerals

Language: English

Topic: Stability and Controllability of Differential Equations

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,190

Funder: King Fahd University of Petroleum and Minerals