Stability of strong global and exponential attractors for semilinear beam equations with fractional damping and memory
Abstract
This paper investigates the stability of strong global and exponential attractors for a semilinear beam equation with memory and fractional damping, where α∈[0,2] denotes the fractional damping exponent and β∈[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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BibTeX
@misc{duan2026stability,
title = {{Stability of strong global and exponential attractors for semilinear beam equations with fractional damping and memory}},
author = {Yu-Ying Duan and Ti-Jun Xiao},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.23002},
eprint = {2609.23002},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.23002},
}
RIS
TY - UNPB
TI - Stability of strong global and exponential attractors for semilinear beam equations with fractional damping and memory
AU - Yu-Ying Duan
AU - Ti-Jun Xiao
PY - 2026
DA - 2026/09/19
PB - arXiv
DO - 10.48550/arxiv.2609.23002
UR - https://arxiv.org/abs/2609.23002
AB - This paper investigates the stability of strong global and exponential attractors for a semilinear beam equation with memory and fractional damping, where α∈[0,2] denotes the fractional damping exponent and β∈[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.
ER -