Long Time Behavior Of Solution For A Class Of High-order Kirchhoff Equation

In this thesis,we study the long time behavior of solutions to the initial boundary value problem for a class of nonlinear High-order Kirchhoff equations with strong damping:utt+(-△)mut +(α +β||▽mu||2)q(-△)mu+g(u)= f(x).Under the assumptions and the use of Galerkin method,we can prove the equation has weak solution(u,ut＋εu)E L∞(0,+∞;H0m(Ω)× L2(Ω))with sufficiently small constantε when the system is degenerate.When the system is non-degenerate,there is a unique solution to the equation(u,ut +εu)∈ L∞(0,+∞;IIm0(Ω)×L2(Ω)).And there is an integral attractor for the operator solution semigroup generated by the solution space.In addition,we prove that the equation has a finite Hausdorff dimension with 0<a<1,β→0.On this basis,it is further proved that there exists exponential attractor about the solution semigroup.