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Portugaliae Mathematica

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Volume 75, Issue 3/4, 2018, pp. 313–327
DOI: 10.4171/PM/2021

Published online: 2019-06-06

Slowly non-dissipative equations with oscillating growth

Phillipo Lappicy[1] and Juliana Pimentel[2]

(1) Universidade de São Paulo, São Carlos, Brazil
(2) Universidade Federal do Rio de Janeiro, Brazil

The goal of this paper is to construct explicitly the global attractors of semilinear parabolic equations when the reaction term has an oscillating growth. In this case, solution can also grow-up, and hence the attractor is unbounded and induces a flow at infinity. In particular, we construct heteroclinic connections between bounded and/or unbounded hyperbolic equilibria when the reaction term is asymptotically linear.

Keywords: Semilinear parabolic equations, infinite dimensional dynamical systems, growup, unbounded global attractor, Sturm attractor

Lappicy Phillipo, Pimentel Juliana: Slowly non-dissipative equations with oscillating growth. Port. Math. 75 (2018), 313-327. doi: 10.4171/PM/2021