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arXiv · 2609.23002

Stability of strong global and exponential attractors for semilinear beam equations with fractional damping and memory

Yu-Ying Duan·Ti-Jun Xiao
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Abstract

This paper investigates the stability of strong global and exponential attractors for a semilinear beam equation with memory and fractional damping, where $α\in[0,2]$ denotes the fractional damping exponent and $β\in[0,1]$ the memory parameter. After showing the existence of a strong global attractor, we prove its upper semicontinuity in the parameter pair $(α,β)$. We then construct a family of strong exponential attractors and establish its continuity in $(α,β)$. Here, ``strong" means that the compactness, attraction, and parameter-robustness properties are established in a topology stronger than that of the phase space. Compared to existing $β= 0$ results, our findings hold in a stronger topology. The analysis draws upon our recent higher-order regularity results for global attractors.

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Yu-Ying Duan, Ti-Jun Xiao. 2026-09-19. Stability of strong global and exponential attractors for semilinear beam equations with fractional damping and memory. https://arxiv.org/abs/2609.23002

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