Existence Of Pullback Attractors For Non-autonomous Kirchhoff-type Suspension Bridge Equations

In this master dissertation, we mainly study the existence of pullback attrac-tors of the non-autonomous suspension bridge equations with strong damping, we apply non-autonomous infinite dimensional dynamical systems and the theorem of pullback attractors to our work. In the end, we get a essential theorem with the non-linearity f(u,t) and a forcing term g(x,t), and f(u,t) is translation bounded. We also prove the compactness of the solutions, and establish the pullback D-attractor in Eo based on the condition-(C), we get a series of new results at the end of the paper.In chapter 1, we introduce the history and development of a dynamical system, the concepts and theorem of pullback attractors and the main methods and thoughts applied in this paper.In chapter 2, we present some preliminary definitions and preliminary results.In chapter 3, we prove the existence of pullback attractors above non-autonomous suspension bridge equations with a strong damping utt+Δ2u+Δ2u+(p-|▽u|2) Δu+ k2u++f(u)= g(x, t), and a nonlinearity f(u). Combining the Faedo-Galerkin method, we get the existence and uniqueness of the weak solution. In the end, we prove the existence of pullback D-attractors with a method of pullback D-condition (C).In chapter 4, we obtain the existence of pullback attractors for the Suspension Bridge Equation with a strong damping in bounded domains as the following equa-tion:utt+Δ2u+Δ2ut+(p-|▽u|2)Δu+k2u++f(u,t)=g(x,t), Combining the Faedo-Galerkin method, we get the existence and uniqueness of the weak solu-tion. In the end, we prove the existence of pullback D-attractors with a method of pullback D-condition (C).