# American Institute of Mathematical Sciences

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February & March  2007, 18(2&3): 483-497. doi: 10.3934/dcds.2007.18.483

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

 1 Dpto. Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160, 41080-Sevilla, Spain 2 Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom 3 Departamento de Matemática Aplicada, Universidad Complutense de Madrid, Madrid 28040, Spain 4 Departamento de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1036,41080–Sevilla, Spain

Received  April 2006 Revised  September 2006 Published  March 2007

The goal of this work is to study the forward dynamics of positive solutions for the non-autonomous logistic equation $u_{t}-\Delta u=\lambda u-b(t)u^{p}$, with $p>1$, $b(t)>0$, for all $t\in \mathbb{R}$, $\lim_{t\to \infty }b(t)=0$. While the pullback asymptotic behaviour for this equation is now well understood, several different possibilities are realized in the forward asymptotic regime.
Citation: José A. Langa, James C. Robinson, Aníbal Rodríguez-Bernal, A. Suárez, A. Vidal-López. Existence and nonexistence of unbounded forwards attractor for a class of non-autonomous reaction diffusion equations. Discrete & Continuous Dynamical Systems - A, 2007, 18 (2&3) : 483-497. doi: 10.3934/dcds.2007.18.483
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