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This work is devoted to the study of the asymptotic behavior of nonautonomousreaction-diffusion equations in Dumbbell domains $\Omega_{\varepsilon} \subset\mathbb{R}^{N}$. Each $\Omega_{\varepsilon}$ is the union of a fixed open set$\Omega$ and a channel $R_{\varepsilon}$ that collapses to a line segment $R_0$as $\varepsilon \rightarrow 0^{+}$. We first establish the global existence ofsolution for each problem by using two properties of the parabolic equationconsidered, which are the positivity of the solutions and comparison resultsfor them. We prove the existence of pullback and uniform attractors and weobtain uniform bounds (in $\varepsilon$) for them.

Pullback and uniform attractors for nonautonomous reaction-diffusion equation in Dumbbell domains