| Full text | |
| Author(s): |
Bruschi, Simone M.
;
Carvalho, Alexandre N.
;
Pimentel, Juliana F.
Total Authors: 3
|
| Document type: | Journal article |
| Source: | Indiana University Mathematics Journal; v. 69, n. 2, p. 657-683, 2020. |
| Web of Science Citations: | 0 |
| Abstract | |
The aim of this article is to provide a relation between the well-known class of dissipative equations and the recently introduced class of slowly non-dissipative equations, in the setting of scalar reaction-diffusion equations. The latter type of equations is characterized by the existence of ``grow-up{''} (i.e., infinite time blowup) with absence of finite time blowup. A particular small perturbation of an unbounded non-dissipative global attractor is considered, in such a way that the perturbed attractor is dissipative. Although the continuity of the family of attractors is verified in compact sets, our choice of perturbation produces a great change on the dynamics close to the infinity of the phase space. In other words, we prove that the limit of the compact attractors is not the unbounded attractor of the limiting equation. (AU) | |
| FAPESP's process: | 14/03685-7 - Continuity of attractors for semilinear parabolic equations |
| Grantee: | Juliana Fernandes da Silva Pimentel |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |
| 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 |