Long Time Behavior Of A Class Of Generalized Kirchhoff-Sine-Gordon Equation

In this paper,we study the initial boundary value problem for a class of generali zed nonlinear Kirchhoff-Sine-Gordon ??? the solution of the long time behavior.This paper prove the existence and uniqueness of the global solution of the above equation by using a priori estimates and Galerkin finite element method,obtain the existence of global attractor,on this basis,we study the finite Hausdorff dimension estimation and the Fractal dimension of the global attr actor.Then prove that the Lipschitz property and the initial boundary value problem f or nonlinear semigroups and squeezing properties are obtained for the exponential attra ctors and subsequently use the method of graph change existence of inertial manifolds of the initial boundary value.Where ? is a bounded domain of Rn?n?1?with a smooth boundary????,? is the dissipation coefficient,? is a positive constant,f?x?,u₀?x?,u)1?x?is a known func tion,and f?x?is the external interference.,Nonlinear function ??s?? C¹[0,?),g?s?? C²?R?.