Time-dependent uniform upper semicontinuity of pullback attractors for non-autonomous delay dynamical systems: Theoretical results and applications

Zhang, Qiangheng; Caraballo, Tomás; Yang, Shuang

doi:10.1090/proc/16937

Time-dependent uniform upper semicontinuity of pullback attractors for non-autonomous delay dynamical systems: Theoretical results and applications
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by Qiangheng Zhang, Tomás Caraballo and Shuang Yang;

Proc. Amer. Math. Soc. 152 (2024), 4809-4820

DOI: https://doi.org/10.1090/proc/16937

Published electronically: September 10, 2024

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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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