| Texto completo | |
| Autor(es): |
Banaskiewicz, Jakub
;
Carvalho, Alexandre N.
;
Garcia-Fuentes, Juan
;
Kalita, Piotr
Número total de Autores: 4
|
| Tipo de documento: | Artigo Científico |
| Fonte: | Journal of Dynamics and Differential Equations; v. N/A, p. 54-pg., 2022-12-26. |
| Resumo | |
If the semigroup is slowly non-dissipative, i.e., its black solutions can diverge to infinity as time tends to infinity, one still can study its dynamics via the approach by the unbounded attractors-the counterpart of the classical notion of global attractors. We continue the development of this theory started by Chepyzhov and Goritskii (Unbounded attractors of evolution equations. Advances in Soviet mathematics, American Mathematical Society, Providence, 1992). We provide the abstract results on the unbounded attractor existence, and we study the properties of these attractors, as well as of unbounded omega-limit sets in slowly non-dissipative setting. We also develop the pullback non-autonomous counterpart of the unbounded attractor theory. The abstract theory that we develop is illustrated by the analysis of the autonomous problem governed by the equation u(t)=Au+f(u). In particular, using the inertial manifold approach, we provide the criteria under which the unbounded attractor coincides with the graph of the Lipschitz function, or becomes close to the graph of the Lipschitz function for large argument. (AU) | |
| Processo FAPESP: | 20/14075-6 - Sistemas dinâmicos e seus atratores sob perturbação |
| Beneficiário: | Alexandre Nolasco de Carvalho |
| Modalidade de apoio: | Auxílio à Pesquisa - Temático |