Stability of strong global and exponential attractors for semilinear beam equations with fractional damping and memory
Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Duan, Yu-Ying, Xiao, Ti-Jun
Institutions: Fuyang Normal University, Fudan University
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
Awards: G274163410, G684715726
OpenAlex ID: W7214039365