We consider the Kirchhoff equations
\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 > \tau ,\\u(x,t)=0,x\in \partial \Omega ,t > \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.
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