| Full text | |
| Author(s): |
Total Authors: 3
|
| Affiliation: | [1] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Campus Sao Carlos, Caixa Postal 668, BR-13560970 Sao Carlos, SP - Brazil
[2] Univ Warwick, Math Inst, Coventry CV4 7AL, W Midlands - England
[3] Univ Seville, Fac Matemat, Dept Ecuac Diferenciales & Anal Numer, E-41012 Seville - Spain
Total Affiliations: 3
|
| Document type: | Journal article |
| Source: | COMMUNICATIONS ON PURE AND APPLIED ANALYSIS; v. 19, n. 4, p. 1997-2013, APR 2020. |
| Web of Science Citations: | 0 |
| Abstract | |
We investigate the forwards asymptotic dynamics of non-autonomous differential equations. Our approach is centred on those models for which the vector field is only defined for non-negative times, that is, the laws of evolution are not given, or simply not known, for times before a given time (say time t = 0). We will be interested in the cases for which the `driving' (time shift) semigroup has a global attractor in which backwards solutions are not necessarily unique. Considering vector fields in the global attractor of the driving semigroup allows for a natural way to extend vector fields, defined only for non-negative times, to the whole real line. These objects play a crucial role in the description of the asymptotic dynamics of our non-autonomous differential equation. We will study, in some particular cases, the isolated invariant sets of the associated skew-product semigroup with the aim of characterising the global attractor. We develop an example for which we derive decomposition for the global attractor of skew-product semigroup from the characterisation of the attractor of the associated driving semigroup. (AU) | |
| FAPESP's process: | 18/10997-6 - Robustness of attractors under autonomous or non-autonomous perturbatinos: Structural Stability |
| Grantee: | Alexandre Nolasco de Carvalho |
| Support Opportunities: | Scholarships abroad - Research |