Attractor Of A Class Of Higher-order Kirchhoff Type Equation With Nonlinear Damping Term

In this thesis,we study the long time behavior of the solution to the initial boundary value problem for high order Kirchhoff-type equation with a nonlinear strong damping term:(?)where??R~n,??is a bounded open domain with smooth boundary;?is the outer norm vector;m>1 is a positive integer,here?is the Laplace operator,?(||?~mu||~2),h(u_t)is a nonlinear damped,f(x)is a function specified later,(-?)~mu_tis a strongly damping term;In this thesis,firstly,we make reasonable assumption about the nonlinear term?(||?~mu||~2),h(u_t).next,we prove the existence and uniqueness of the solution by using the priori estimate and Galerkin method,obtain the semigroup of the operator solution,further obtain the global attractor;then,the upper bound of the Hausdorff dimension of the global attractor is discussed;finally,the exponential attractor of the Kirchhoff equation is obtained.