Time-dependent uniform upper semicontinuity of pullback attractors for non-autonomous delay dynamical systems: Theoretical results and applications
Qiangheng Zhang, Tomás Caraballo, Shuang Yang
Source abstract
In this paper we provide general results on the uniform upper semicontinuity of pullback attractors with respect to the time parameter for non-autonomous delay dynamical systems. Namely, we establish a criteria in terms of the multi-index convergence of solutions for the delay system to the non-delay one, locally pointwise convergence and local controllability of pullback attractors. As an application, we prove the upper semicontinuity of pullback attractors for a non-autonomous delay reaction-diffusion equation to the corresponding nondelay one over any bounded time interval as the delay parameter tends to zero.
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