Global Existence,Asymptotic Behavior And Uniform Attractors For A Non-autonomous Timoshenko System Of Type Ⅲ With Weak Damping

In this paper,we investigate one-dimensional thermoelastic system of Timoshenko type III with double memory dampings.At first we give the global existence of solutions by using semigroup theory.Then we prove the energy decay of solutions by constructing a series of multiplier equations and Lyapunov function and can obtain the existence of absorbing ball.Finally,a suitable symbol space ∑ is selected to obtain the process family UF(t,τ),Then the uniform asymptotic compactness of process family UF(t,τ)is proved by using the method of uniform compression function,and the existence of uniform attractor is obtained.