Global existence, asymptotic behavior and uniform attractors for a non-autonomous Timoshenko system of thermoelasticity of type III with a time-varying delay. (English) Zbl 1428.35581
Summary: In this paper, we first establish the global existence by using the variable norm technique of Kato and semigroup method. Second, under suitable assumptions on the data, we obtain the asymptotic behavior of the solution. Last, we prove the existence of a uniform attractor by using the method of uniform contractive functions.
MSC:
| 35Q74 | PDEs in connection with mechanics of deformable solids |
| 74F05 | Thermal effects in solid mechanics |
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 35B41 | Attractors |
| 35L53 | Initial-boundary value problems for second-order hyperbolic systems |
| 37L30 | Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems |
| 47D06 | One-parameter semigroups and linear evolution equations |
Keywords:
Timoshenko system; global existence; asymptotic behavior; uniform attractors; semigroup methodReferences:
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