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- Title
The global attractor for a class of extensible beams with nonlocal weak damping.
- Authors
Zhao, Chunxiang; Zhao, Chunyan; Zhong, Chengkui
- Abstract
The goal of this paper is to study the long-time behavior of a class of extensible beams equation with the nonlocal weak dampingutt+Δ2u−m(∥∇u∥2)Δu+∥ut∥put+f(u)=h,inΩ×R+,p≥0on a bounded smooth domain Ω⊂Rn with hinged (clamped) boundary condition. Under some suitable conditions on the Kirchhoff coefficient m(∥∇u∥2) and the nonlinear term f(u), the well-posedness is established by means of the monotone operator theory and the existence of a global attractor is obtained in the subcritical case, where the asymptotic smooothness of the semigroup is verified by the energy reconstruction method.
- Publication
Discrete & Continuous Dynamical Systems - Series B, 2020, Vol 25, Issue 3, p935
- ISSN
1531-3492
- Publication type
Academic Journal
- DOI
10.3934/dcdsb.2019197