Attractors and upper semicontinuity for an extensible beam with nonlocal structural damping
Abstract
Abstract We analyze the asymptotic behavior of a class of extensible beam models governed by a nonlocal structural damping mechanism of the form , where . The coefficient is a degenerate ‐function depending on the linear energy of the system and determines the intensity of the damping. Our main result establishes that, for each , the ‐semigroup generated by the weak solutions of the problem admits a compact global attractor , where denotes the unstable manifold emanating from the set of stationary points. Moreover, we show the upper semicontinuity of the family of global attractors with respect to the fractional exponent .
Fields of Study & Subjects
Stability and Controllability of Differential Equations
Vibration and Dynamic Analysis
Nonlinear Differential Equations Analysis
Publication details
- Journal / source
- ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik
- Volume
- 106
- Issue
- 2
- Publication date
- 1 February 2026
- Language
- EN