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arXiv · 2610.13068

Uniform Exponential Attractors for Non-Autonomous Dynamical Systems and an Application to the damped hyperbolic equation with sub-quintic growth

Chang Qingquan·Li Dandan
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Abstract

In this paper, we develop an abstract framework for the theory of uniform exponential attractors in non-autonomous dynamical systems. Our construction employs time-dependent absorbing sets while ensuring exponential attraction among the constructed sets. Moreover, we show that the resulting exponential attractors are uniform-that is, they remain stable under perturbations. As an application of this abstract theory, we study the weakly damped hyperbolic equation with sub-quintic nonlinearity. Using the proposed approach, we construct exponential attractors for the process generated by the Shatah-Struwe solution, which satisfies both energy and Strichartz estimates. Furthermore, we establish the Holder continuity of these exponential attractors with respect to the external forcing term.

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Chang Qingquan, Li Dandan. 2026-10-09. Uniform Exponential Attractors for Non-Autonomous Dynamical Systems and an Application to the damped hyperbolic equation with sub-quintic growth. https://arxiv.org/abs/2610.13068

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