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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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Cite

BibTeXRIS
BibTeX
@misc{qingquan2026uniform,
  title = {{Uniform Exponential Attractors for Non-Autonomous Dynamical Systems and an Application to the damped hyperbolic equation with sub-quintic growth}},
  author = {Chang Qingquan and Li Dandan},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.13068},
  eprint = {2610.13068},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.13068},
}
RIS
TY  - UNPB
TI  - Uniform Exponential Attractors for Non-Autonomous Dynamical Systems and an Application to the damped hyperbolic equation with sub-quintic growth
AU  - Chang Qingquan
AU  - Li Dandan
PY  - 2026
DA  - 2026/10/09
PB  - arXiv
DO  - 10.48550/arxiv.2610.13068
UR  - https://arxiv.org/abs/2610.13068
AB  - 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.
ER  -