论文标题
哑铃域中非自主反应扩散方程的回调和统一吸引子
Pullback and uniform attractors for nonautonomous reaction-diffusion equation in Dumbbell domains
论文作者
论文摘要
这项工作致力于研究哑铃域中非自主反应 - 扩散方程$ω_ {\ varepsilon} \ subset \ subset \ mathbb {r}^{n} $的渐近行为。每个$ω_ {\ varepsilon} $都是固定的打开集$ω$的结合，而通道$ r _ {\ varepsilon} $倒在线段$ r_0 $ as $ \ varepsilon \ varepsilon \ rightArrow 0^{+} $。我们首先通过使用所考虑的抛物线方程的两个属性来建立每个问题的全局解决方案的存在，这是解决方案的积极性和它们的比较结果。我们证明了回调和统一吸引子的存在，并为它们获得了统一的界限（以$ \ varepsilon $为单位）。
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.
