Abstract: In this talk we shall study the dynamics of semilinear non-autonomous evolution equations in which the linear operator is a time-dependent family of uniformly almost sectorial operators, that is, problems of the form
\begin{equation}\label{eq1}
\begin{cases}
u'(t) = -A(t) + f(u), t > \tau \\
u(\tau)=u_0
\end{cases}\end{equation}
We prove existence, uniform bounds and upper semicontinuity of pullback attractors for a reaction-diffusion equation in Dumbbell domain that generates an abstract evolution equation like \eqref{eq1}.