Global Existence And Asymptotic Behavior For A Timoshenko System Of Thermoelasticity Of Type Ⅲ With A Delay Term And A Thermo-viscoelastic Damping

In this paper,a Timoshenko system with a delay term and a thermo-viscoelastic damping of type Ⅲ subjected to Dirichlet-Dirichlet-Neumann boundary conditions will be considered.Firstly,we establish the global existence by using the new method-semigroup method.Secondly,under suitable assumptions and ρ1/k=ρ2/b,we obtain the asymptotic behavior of the solution by exploiting energy method to produce a suitable Lyapunov functional.