论文标题
非自治非局部扩散方程的时间依赖性吸引子的存在和上半强度
Existence and upper semicontinuity of time-dependent attractors for the non-autonomous nonlocal diffusion equations
论文作者
论文摘要
在本文中，根据一些适当的假设，我们证明了最小时间相关的回调$ \ Mathcald_σ^{\ Mathcal {h} _ {t} _ {t}} $ - 吸引者$ {\ MATHCAL {\ MATHCAL {a}}} _ {时间依赖的空间中的非自治非局部扩散方程$ \ MATHCAL {h} _ {t}（ω）$。接下来，在同一阶段空间中，使用先验的估计和能量方法，我们确定了与时间相关的回拉吸引子的存在$ \ left \ {a_ξ（t）\ right \} _ { $ξ= 0 $的全局吸引子$ a $ a $，即$$ \ lim_ {ξ\ rightarrow 0^{+}}} \ propatoTorname {dist} _ {\ Mathcal H_ {t}}} \ left（a_ped（a_pen），a \ right），a \ right）= 0。 $$
In this paper, under some appropriate assumptions, we prove the existence of the minimal time-dependent pullback $\mathcal D_σ^{\mathcal{H}_{t}}$-attractors ${\mathcal{A}}_{\mathcal D_σ^{\mathcal{H}_{t}}}$ for the non-autonomous nonlocal diffusion equations in time-dependent space $\mathcal{H}_{t}(Ω)$. Next, in same phase space, using a priori estimate and energy methods we establish the existence of time-dependent pullback attractors $\left\{A_ξ(t)\right\}_{t \in \mathbb R}$ and the upper semicontinuity of $\left\{A_ξ(t)\right\}_{t \in \mathbb R}$ and the global attractor $A$ of the equation with $ξ= 0$, that is, $$ \lim_{ξ\rightarrow 0^{+}} \operatorname{dist}_{\mathcal H_{t}}\left(A_ξ(t), A \right)=0. $$
