| Summary: | Abstract In this paper, proving the pullback asymptotic compactness of processes by the aid of a contractive function in space X 0 $X_{0}$ , we prove the existence of a pullback attractor for N-dimensional nonautonomous thermoelastic coupled structure equations u t t + α △ 2 u − [ β + σ ( ∫ Ω ( ∇ u ) 2 d x ) ] △ u + γ △ θ + g ( u ) + η u t = h ( x , t ) , in Ω × [ τ , ∞ ) , θ t − △ θ − γ △ u t = q ( x , t ) in Ω × [ τ , ∞ ) , $$\begin{aligned} &u_{tt}+\alpha\triangle^{2}u-\biggl[\beta+\sigma\biggl( \int_{\Omega}(\nabla u)^{2}\,dx\biggr)\biggr]\triangle u+ \gamma\triangle\theta+g(u)+\eta u_{t}=h(x,t), \\ &\quad \mbox{in } \Omega \times [\tau,\infty), \\ &\theta_{t}-\triangle\theta-\gamma\triangle u_{t}=q(x,t) \quad \mbox{in } \Omega\times [\tau,\infty), \end{aligned}$$ with the lateral load distribution function h ( x , t ) $h(x,t)$ and the external heat supply function q ( x , t ) $q(x,t)$ unnecessarily bounded. The nonlinear source term g ( u ) $g(u)$ is essentially k 1 ( u + | u | ρ − 1 u ρ + 1 ) $k_{1}(u+\frac{|u|^{\rho-1}u}{\rho+1})$ ( k 1 > 0 ) $(k_{1}>0)$ with 1 < ρ ≤ N N − 2 $1<\rho\leq\frac{N}{N-2}$ if N ≥ 3 $N\geq 3$ and 1 < ρ < ∞ $1<\rho<\infty$ if N = 1 , 2 $N=1,2$ .
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