Dynamic Morpholopy Of A Class Of High Order Beam Equations

This paper mainly studies the high order Beam equation with strong damping terms.The existence of the global attractor family of the high order Beam equations is proved by using the prior estimation and Galerkin finite elements method through app--ropriate assumptions.After linearizing the equations,the related dimension estimation is discussed,and the result with finite dimension is obtained.Then the equation is transformed into a random differential equation.The existence of the random attractor family of the high order Beam equation is proved by proving the positive quality and estimation of the operator and decomposing the solution of the equation.Finally,the Lipschitz continuity of nonlinear terms is proved to be valid,and the spectral interval condition of operator is proved to be valid when N is large enough by the method of graph norm transformation,thus the existence of inertia manifold of high order Beam equation is proved.Therefore,the equation has inertia manifold.