A non-autonomous scalar one-dimensional dissipative parabolic problem: the description of the dynamics

Autor(es)

Broche, Rita de Cassia D. S. ^{[1, 2]} ; Carvalho, Alexandre N. ^[3] ; Valero, Jose ^[4]

Afiliação do(s) autor(es)

^[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

• Tipo de documento: Artigo Científico
• Fonte: Nonlinearity; v. 32, n. 12, p. 4912-4941, DEC 2019.
• Citações Web of Science: 0

Resumo

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)

• Processo FAPESP: 03/10042-0 - Sistemas dinâmicos não lineares e aplicações
• Beneficiário: Alexandre Nolasco de Carvalho
• Modalidade de apoio: Auxílio à Pesquisa - Programa PRONEX - Temático