Initial-boundary Value Problem For Higher-order Viscoelastic Equations Of Kirchhoff Type

In this paper,we consider the initial-boundary value problem for some nonlinear higher-order viscoelastic Kirchhoff type equations.By using Banach contraction fixed point theorem,we study the existence and uniqueness of local solutions for some higher-order viscoelastic Kirchhoff type equations with source terms.Meanwhile,the blow-up and lifespan estimates of solutions are also given according to Lyapunov inequality.By means of energy estimation method and the continuous boundedness criterion,we prove the existence of global solutions for higher-order viscoelastic Kirchhoff equation with damping term and establish the decay property of global solutions by applying the difference inequality due to Nakao.