| In this paper,we study of nonlinear wave equation with strong fourth order dissipationwhere α>0,x∈Ω,t∈[0,+∞), Ω is a bounded domain with smooth boundary.(?)Ω is the boundary of Ω.g(u) is the nonlinear term.f(x) is the external force term.In order to prove the existence of global attractor of the equation, First we give the priori estimates to abtain the existence and uniqueness of wave equations with four strong dissipative term. And then we define the solution semigroup on the basis of this, We also get the tight absorbing set, Then finally we study the continuity of solution semigroups, At last, we use the Hadamard graph transformation method to prove the existence of inertial manifold. In this paper, we study of the nonlinear wave equation with strong fourth order dissipation of the existence of attractor and its inertia with the follow four chapters:Chapter1:Mainly introduced the nonlinear wave equation and its research status;Chapter2:Mainly introduced some basic knowledge that used in this paper and some commonly used inequalities;Chapter3:Mainly introduced the existence and uniqueness of the solution of the nonlinear wave equation with strong dissipative term, and the existence of global attractor;Chapter4:Mainly introduced the inertial manifold of the nonlinear wave equation with strong dissipative term. |
