A Gronwall-type lemma with parameter and its application to Kirchhoff type nonlinear wave equation

The paper investigates a new Gronwall-type lemma with parameter ϵ>0, and establishes the uniform-in-time estimates. As an application, the paper studies the asymptotic behavior of the Kirchhoff-type equations with a strong dissipation, and proves that the related solution semigroup possesses the global attractor.