Longtime dynamics for a class of extensible beams with degenerate nonlocal damping
Abstract
In this paper, we investigate the long-time dynamics of a class of extensible beams equation with the degenerate nonlocal damping $ u_{tt}+\Delta^2 u-m(\|\nabla u\|^2)\Delta u -\left \| \nabla u_{t} \right \| ^{p} \Delta u _{t} +f(u) = h, \;{\rm{in}}\;\; \Omega\times\mathbb{R^{+}}, $ with hinged (clamped) boundary condition. Due to the effect of nonlocal damping, we are concerned with the well-posedness of the solutions and the existence of a global attractor when the growth exponent $ \rho $ of the source terms satisfies $ 1
Fields of Study & Subjects
Stability and Controllability of Differential Equations
Advanced Mathematical Physics Problems
Nonlinear Partial Differential Equations
Publication details
- Journal / source
- Discrete and Continuous Dynamical Systems - B
- Volume
- 36
- Issue
- 0
- Pages
- 108–134
- Publication date
- 1 January 2026