The Attractor Of A Class Of Higher-order Kirchhoff-type Equation

In this thesis,we investigate the global well-posedness and the global attractors and exponential attractors of the solution for the Higher-order Kirchhoff-type equation with strongly nonlinear damping:(?) where W is a bounded domain of Rn,with a smooth dirichlet boundary ?W and initial value,n is the unit outward normal on ?W,and m is a positive integer greater than 1.Moreover,Nonlinear strongly dampings(s)and f(s)are scalar functions,f is the external interference.According to the hypothesis,the existence and uniqueness of the solution are proved by using priori estimates and Galerkin method,then we get the global attractors.On this basis,the existence of exponential attractor is proved by discussing the squeezing property of the nonlinear semigroup associated with this equation.By investigate the global attractors and exponential attractors of the above equation,we also discuss the pullback attractors for the Higher-order Kirchhoff-type equation with nonlinear strongly damping and delays:(?)For this equation,a strong solution decomposition method is used to prove the existence and uniqueness of the solution,further more,the existence of the pullback attractor is proved.