Dumbbell区域上非自治反应扩散方程的拉回吸引子和一致吸引子
Pullback and uniform attractors for nonautonomous reaction-diffusion equation in Dumbbell domains
摘要：
本文研究了Dumbbell区域上非自治反应扩散方程$Ω_{\varepsilon} \subset \mathbb{R}^{N}$的渐近性态。每个$Ω_{\varepsilon}$是固定开集$Ω$和通道$R_{\varepsilon}$的并集，通道$R_{\varepsilon}$折叠成线段$R_0$作为$\varepsilon \rightarrow 0^{+}$。首先利用所考虑的抛物型方程的两个性质，即解的正性和它们的比较结果，证明了每个问题解的整体存在性.我们证明了拉回和一致吸引子的存在性，并得到了它们的一致界（在$\varepsilon$中）。
英文摘要：
This work is devoted to the study of the asymptotic behavior of nonautonomous reaction-diffusion equations in Dumbbell domains $Ω_{\varepsilon} \subset \mathbb{R}^{N}$. Each $Ω_{\varepsilon}$ is the union of a fixed open set $Ω$ and a channel $R_{\varepsilon}$ that collapses to a line segment $R_0$ as $\varepsilon \rightarrow 0^{+}$. We first establish the global existence of solution for each problem by using two properties of the parabolic equation considered, which are the positivity of the solutions and comparison results for them. We prove the existence of pullback and uniform attractors and we obtain uniform bounds (in $\varepsilon$) for them.
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