| Full text | |
| Author(s): |
Total Authors: 3
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| Affiliation: | [1] Univ Sao Paulo, Sao Carlos, SP - Brazil
[2] Univ Fed Lavras, Dept Ciencias Exatas, Caixa Postal 3037, BR-37200000 Lavras, MG - Brazil
[3] Univ Sao Paulo, Dept Matemat, Inst Ciencias Matemat & Comp, Sao Carlos, SP - Brazil
[4] Univ Miguel Hernandez Elche, Ctr Invest Operat, Avda Univ S-N, Alicante 03540 - Spain
Total Affiliations: 4
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| Document type: | Journal article |
| Source: | Nonlinearity; v. 32, n. 12, p. 4912-4941, DEC 2019. |
| Web of Science Citations: | 0 |
| Abstract | |
The purpose of this paper is to give a characterization of the structure of non-autonomous attractors of the problem u(t) = u(xx) + lambda u - beta(t)u(3) when the parameter lambda > 0 varies. Also, we answer a question proposed in Carvalho et al (2012 Proc. Am. Math. Soc. 140 2357-73), concerning the complete description of the structure of the pullback attractor of the problem when 1 < lambda < 4 and, more generally, for lambda not equal N-2, 2 <= N is an element of N. We construct global bounded solutions, `non-autonomous equilibria', connections between the trivial solution and these `non-autonomous equilibria' and characterize the alpha-limit and omega-limit set of global bounded solutions. As a consequence, we show that the global attractor of the associated skew-product flow has a gradient structure. The structure of the related pullback an uniform attractors are derived from that. (AU) | |
| FAPESP's process: | 03/10042-0 - Nonlinear dynamical systems and applications |
| Grantee: | Alexandre Nolasco de Carvalho |
| Support Opportunities: | PRONEX Research - Thematic Grants |