Asymptotic Behavior Of Solutions For A Class Of Nonlinear High-order Kirchhoff-type Equations

In this paper,we study a class of nonlinear nonlocal Kirchhoff-type high-order partial differential equations of progressive state problem.Given the appropriate assumptions,at first,we use the prior-estimation and Galerkin method to prove the equation in space H₀^m(10)k(?)?H₀^k(?)existence a unique global solution,then compact method is used to prove the existence of the semigroup generated solutions S(t)have a whole attactor family_kA;Secondly,through the linearization method,the Frechet differentiability of operator semigroupS(t)and the attenuation of volume element in the linearization problem are proved,so as to obtain the Hausdorff dimension and Fractal dimension estimation of the whole attractor family;Finally,the external termf(x)of the problem is transformed into a random termq(x)W(5),and the weak solution of the equation for the Ornstin-Uhlenbeck process is used to deal with the random term of the nonlinear nonlocal higher-order Kirchhoff-Type with additive white noise,a bounded random absorbing set is obtained and the existence of random attractor family is proved by Isomorphism mapping method.