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- Title
Well‐posedness and dynamics for the von Karman equation with memory and nonlinear time‐varying delay.
- Authors
Cui, Xiaona; Li, Ke
- Abstract
This paper is concerned with mathematical analysis for the viscoelastic von Karman equation with memory and time‐varying delay. Based on the existence and uniqueness of the strong solution established by Galerkin method, the finite dimensional global attractor for the system without time‐varying delay has been shown by using the quasi‐stability theory. The difficulties for our desired well‐posedness are the limiting of fourth‐order derivative terms and the von Karman bracket term, which need some delicate estimates to achieve. The key point for the dynamics is to obtain the quasi‐stability for gradient system, which needs the higher regularity of trajectory especially the von Karman bracket.
- Subjects
VON Karman equations; NONLINEAR equations; MATHEMATICAL analysis; GALERKIN methods; TIME-varying systems
- Publication
Mathematical Methods in the Applied Sciences, 2023, Vol 46, Issue 14, p15481
- ISSN
0170-4214
- Publication type
Article
- DOI
10.1002/mma.9389