Long-time behavior for evolution processes associated with Kirchhoff equations with time-dependent coefficients

We consider the Kirchhoff equations　　 \qquad\begincases (\alpha (t)u_t)_t-\phi (\left|\left|\nabla u\right|\right|^2)\Delta u+\gamma (t)u_t+\delta (t)u=\phi (\left|\left|\nabla u\right|\right|^2)f(u),x\in \Omega ,t \gt \tau ,\\u(x,t)=0,x\in \partial \Omega ,t \gt \tau ,\\u(x,\tau )=u_\tau (x),u_t(x,\tau )=v_\tau (x),x\in \Omega ,\endcases where \Omega is a bounded smooth domain in \mathbfR^N , N\geq 3,\tau \in \mathbfR , f is a real valued function of a real variable with some suitable conditions of growth, regularity and dissipativity, \alpha ,\gamma ,\delta are continuous real valued functions of a real variable with some suitable conditions of growth, regularity. we obtain a result of local solvability for the problem using the theory of nonlinear evolution process from non-autonomous hyperbolic problems. By applying a suitable time rescaling transformation we prove the existence and upper semicontinuity of the pullback attractors initial-boundary value problem in a suitable space.