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

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.