Robust Pullback and Exponential Pullback Attractors for Thermoelastic Plates

What is it about?

This paper investigates the robustness of pullback and exponential pullback attractors for a non-autonomous thermoelastic plate with p-Laplacian under the Coleman-Gurtin heat theory. The existence of pullback attractors in the natural space energy with finite dimensionality is proved, along with its upper semicontinuity and continuity with respect to the damped parameter α ∈ [0, 1]. The paper also proves that the related process has a pullback exponential attractor Mα exp and its Hölder continuity on α ∈ [0, 1]. The results extend those of previous research by Fatori et al. (2015).

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Why is it important?

This research is important because it deepens and extends the results of recent studies on pullback attractors, their existence, and robustness in the context of non-autonomous thermoelastic plates with p-Laplacian under the Coleman-Gurtin heat theory. Such studies have practical applications in understanding and predicting the behavior of complex systems in various fields, including engineering, physics, and biology. Key Takeaways: 1. The paper investigates the existence and robustness of pullback and exponential pullback attractors for non-autonomous thermoelastic plates with p-Laplacian under the Coleman-Gurtin heat theory. 2. The study provides a better understanding of the long-term behavior and stability of these systems, which is crucial for making accurate predictions and improving control strategies. 3. The research contributes to the literature on pullback attractors, extending and deepening the results of previous studies in this area.