| Full text | |
| Author(s): |
Cui, Hongyong
;
Figueroa-Lopez, Rodiak N.
;
Langa, Jose A.
;
Nascimento, Marcelo J. D.
Total Authors: 4
|
| Document type: | Journal article |
| Source: | SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS; v. 23, n. 3, p. 37-pg., 2024-01-01. |
| Abstract | |
In this paper we studied the forward dynamics of nonautonomous dynamical systems in terms of forward attractors. We first reviewed the well-known uniform attractor theory, and then by weakening the uniformity of attraction we introduced semiuniform forward attractors and minimal (nonuniform) forward attractors. With these semiuniform attractors, a characterization of the structure of uniform attractors was given: a uniform attractor is composed of two semiuniform attractors and bounded complete trajectories connecting them. As a consequence, the nature of the forward attraction of a dissipative nonautonomous dynamical system was then revealed: the vector field in the distant future of the system determines the (nonuniform) forward asymptotic behavior. A criterion for certain semiuniform attractors to have finite fractal dimension was given and the finite dimensionality of uniform attractors was discussed. Forward attracting time-dependent sets were studied also. A sufficient condition and a necessary condition for a time-dependent set to be forward attracting were given with illustrative counterexamples. Forward attractors of a Navier-Stokes equation with asymptotically vanishing viscosity (with an Euler equation as the limit equation) and with time-dependent forcing were studied as applications. (AU) | |
| FAPESP's process: | 20/14075-6 - Dynamical systems and their attractors under perturbations |
| Grantee: | Alexandre Nolasco de Carvalho |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 22/16305-4 - Long-time dynamics of semilinear problems |
| Grantee: | Marcelo José Dias Nascimento |
| Support Opportunities: | Regular Research Grants |