Global existence and general decay results for a Kirchhoff-type system with nonlinear frictional damping and logarithmic source terms

In this paper, we consider a system of coupled wave equations of Kirchhoff-type with logarithmic source terms. The system is dissipated using two nonlinear frictional-type damping terms, which act within the domain and are modulated by a time-dependent coefficient. We examine the interaction between the damping mechanisms and the logarithmic source terms under specific conditions. Using the standard Faedo–Galerkin method and the potential well approach, we prove the global existence of solutions to the system. The stability of the system is proved using the multiplier method and some properties of convex functions and logarithmic inequalities. We establish general decay results in which exponential and polynomial decay are special cases. Our results are derived without imposing any restrictive growth assumptions on the nonlinear frictional damping terms. Furthermore, our decay rates depend on the nonlinear frictional damping terms, the logarithmic source terms, and the time-dependent coefficient. The findings in this paper significantly improve and generalize earlier results in the literature.