论文标题
在时间依赖的空间和应用中吸引子的连续性
Continuity of the attractors in time-dependent spaces and applications
论文作者
论文摘要
在本文中，我们研究了吸引子在时间依赖的相位空间中的连续性。 （i）我们建立了两个关于上半年性的抽象标准，以及在扰动方面的回调$ \ mathscr d $ - 吸引者的剩余连续性，以及其连续性和其连续性与回拔等式的等价标准，这是在[27,28]中开发的吸引者的连续性理论，以在[27,28]中开发到时间依赖于时间依赖于时空的空间。 （ii）我们提出了回调$ \ mathscr d $ - 表达吸引子的概念，其中包括与时间相关的指数吸引子[33]作为其空间案例的概念，并确定其存在，并通过Quasi-stybilition通过准稳定性方法最初由Chueshov和Lasiecka介绍。 （iii）我们将上述标准应用于半连接阻尼的波动方程，并具有扰动的时间相关的传播速度：$ \eρ（t）u_ {tt}+αu_t}+αU_T-ΔU+f（u）= g $，带有触发参数$ \ e \ in（0）$ in（in（0）$ in（in）$ \ in（上面） $ \ MATHSCR D $ - 指数吸引者在时间依赖的相位空间中，此处开发的方法可以克服模型的双曲线的难度，并扩大了文献中时间相关空间中吸引者的最新理论[15,20,19]。
In this paper, we investigate the continuity of the attractors in time-dependent phase spaces. (i) We establish two abstract criteria on the upper semicontinuity and the residual continuity of the pullback $\mathscr D$-attractor with respect to the perturbations, and an equivalence criterion between their continuity and the pullback equi-attraction, which generalize the continuity theory of attractors developed recently in [27,28] to that in time-dependent spaces. (ii) We propose the notion of pullback $\mathscr D$-exponential attractor, which includes the notion of time-dependent exponential attractor [33] as its spacial case, and establish its existence and Hölder continuity criterion via quasi-stability method introduced originally by Chueshov and Lasiecka [12,13]. (iii) We apply above-mentioned criteria to the semilinear damped wave equations with perturbed time-dependent speed of propagation: $\eρ(t) u_{tt}+αu_t -Δu+f(u)=g$, with perturbation parameter $\e\in(0, 1]$, to realize above mentioned continuity of pullback $\mathscr D$ and $\mathscr D$-exponential attractors in time-dependent phase spaces, and the method developed here allows to overcome the difficulty of the hyperbolicity of the model. These results deepen and extend recent theory of attractors in time-dependent spaces in literatures [15,20,19].
