The Time-dependent Global Attractors For Kirchhoff-type Wave Equation With Structural Damping

In this thesis,we investigate the long-time dynamic behavior of solutions to Kirchhoff type wave equation with structural damping in the time-dependent space Ht1=V1×L2(Ω).This thesis mainly studies the two questions as follows:(1)for the Kirchhoff wave equation with structural damping:where θ ∈(1/2,1),M(‖▽‖2)Δu is nonlocal term,f(u)is nonlinear function and g(x)is the external forcing,Ω is a bounded domain with a smooth boundary (?)Ωof R3.Firstly,the well-posedness of the solution of the equation is verified by using Faedo-Galerkin method,and the regularity of the solution is testified by using the asymptotic regularity estimation technique.Secondly,the asymptotic compactance of the process is verified by the modified process theory and the contraction function theory.Finally,we prove the existence of the time-dependent global attractor.(2)for the Kirchhoff wave equation with nonlocal structural damping:where φ(‖▽u‖2)Δu is nonlocal term and σ(‖▽u‖2)(-Δ)θ(?)tu is nonlocal structural damping.We use the same method as problem(1),the existence of a time dependent global attractor is proved.