A Long Time Behavior Of Solution Of Generalized Of High-order Kirchhoff Type Equation

In this paper,we mainly studies the long-term behavior of the initial-boundary value problem of a class of generalized higher-order nonlinear Kirchhoff wave equations.Firstly,we use the Sobolev space theory to make appropriate assumptions for the Kirchhoff stress term N(?Dmu(t)?qq),and use the uniform prior estimation of time and the Galerkin method to obtain the existence and uniqueness of the equation solution.Then,using the Rellich-Kondrachov compact embedding theorem,the solution semigroup generated by the Kirchhoff equation has a family of global attractors in the phase space Ek=H02m+k(?)×H0k(?).Furthermore,it is proved that we understand the Frechet differentiability of the semigroup in space Ek,and estimate the upper bounds of the Hausdorff dimension and Fractal dimension with a family of global attractors,and concluded that its Hausdorff dimension and Fractal dimension are finite.Finally,the higher-order Kirchhoff-type equation is transformed into a first-order development equation,and the graph norm in the space Ek is defined to verify that the operator satisfies the spectral interval condition,and a family of inertial manifold is obtained in space Ek.On this basis,the existence of a family of pullback attractors in the original equation with the addition of time delay term h(ut)is proved.