arXiv subjects

Yu-Ying Duan

Publications and source records attributed to Yu-Ying Duan.

2 recordsLinked to original sources

arXiv2026

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

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.

math.AP↗

arXiv2026

Regularity of global attractors for beam equations with fractional damping and memory

This paper investigates the long-time behavior of a semilinear beam equation in a domain $Ω\subset R^{n}$, with memory and fractional damping of the form $(-Δ)^αu_{t}$ ($α\in [0,2]$ the dissipation index). Two critical growth indices of the nonlinear term are determined for smooth and $C^2$ boundaries respectively, concerning the existence of the associated semigroup. We prove the existence of global attractor for the semigroup by showing that it possesses a bounded absorbing set and asymptotic compactness. Furthermore, we find out a new way to obtain, for all $α$, higher regularities than anticipated for the attractors, and the regularity result indicates an interesting phenomenon that even much weaker damping can produce regularity that is infinitely close to that in the case of strong damping ($α=2$). As a consequence, our regularity result deepens and extends the existing related ones for the case when the memory is absent.

math.AP↗