Existence and nonexistence of unbounded forwards attractor for a class of non-autonomous reaction diffusion equations

J. A. Langa; J. C. Robinson; A. Rodríguez-Bernal; A. Suárez; A. Vldal-López

doi:10.3934/dcds.2007.18.483

Existence and nonexistence of unbounded forwards attractor for a class of non-autonomous reaction diffusion equations

J. A. Langa^*, J. C. Robinson, A. Rodríguez-Bernal, A. Suárez, A. Vldal-López

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

20 Citations (Scopus)

Abstract

The goal of this work is to study the forward dynamics of positive solutions for the non-autonomous logistic equation u_t -△u = λu - b(t)u^p, with p > 1, b(t) > 0, for all t ∈ ℝ lim_t_∞ b(t) -0. While the pullback asymptotic behaviour for this equation is now well understood, several different possibilities are realized in the forward asymptotic regime.

Original language	English
Pages (from-to)	483-497
Number of pages	15
Journal	Discrete and Continuous Dynamical Systems
Volume	18
Issue number	2-3
DOIs	https://doi.org/10.3934/dcds.2007.18.483
Publication status	Published - 2007
Externally published	Yes

Keywords

Non-autonomous reaction diffusion equations
Unbounded forwards attractor

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Langa, J. A., Robinson, J. C., Rodríguez-Bernal, A., Suárez, A., & Vldal-López, A. (2007). Existence and nonexistence of unbounded forwards attractor for a class of non-autonomous reaction diffusion equations. Discrete and Continuous Dynamical Systems, 18(2-3), 483-497. https://doi.org/10.3934/dcds.2007.18.483

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doi = "10.3934/dcds.2007.18.483",

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AU - Langa, J. A.

AU - Robinson, J. C.

AU - Rodríguez-Bernal, A.

AU - Suárez, A.

AU - Vldal-López, A.

PY - 2007

Y1 - 2007

N2 - The goal of this work is to study the forward dynamics of positive solutions for the non-autonomous logistic equation ut -△u = λu - b(t)up, with p > 1, b(t) > 0, for all t ∈ ℝ limt_∞ b(t) -0. While the pullback asymptotic behaviour for this equation is now well understood, several different possibilities are realized in the forward asymptotic regime.

AB - The goal of this work is to study the forward dynamics of positive solutions for the non-autonomous logistic equation ut -△u = λu - b(t)up, with p > 1, b(t) > 0, for all t ∈ ℝ limt_∞ b(t) -0. While the pullback asymptotic behaviour for this equation is now well understood, several different possibilities are realized in the forward asymptotic regime.

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JF - Discrete and Continuous Dynamical Systems

IS - 2-3

ER -

Existence and nonexistence of unbounded forwards attractor for a class of non-autonomous reaction diffusion equations

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Keywords

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