On a Kirchhoff wave model with nonlocal nonlinear damping

This paper is concerned with the well-posedness as well as the asymptotic behavior of solutions for a quasi-linear Kirchhoff wave model with nonlocal nonlinear damping term σ(∫Ω|∇ u|²\,dx )g(uₜ), where σ and g are nonlinear functions under proper conditions. The analysis of such a damping term is presented for this kind of Kirchhoff models and consists the main novelty in the present work.