Time-dependent uniform upper semicontinuity of pullback attractors for non-autonomous delay dynamical systems: theoretical results and applications. (English) Zbl 07928599
Summary: 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.
MSC:
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 35B41 | Attractors |
| 37L15 | Stability problems for infinite-dimensional dissipative dynamical systems |
| 37L30 | Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems |
Keywords:
uniform upper semicontinuity; pullback attractor; multi-index convergence; delay; reaction-diffusionReferences:
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