Structure and bifurcation of pullback attractors in a non-autonomous Chafee-Infante equation

Authors:
A. N. Carvalho, J. A. Langa and J. C. Robinson

Journal:
Proc. Amer. Math. Soc. **140** (2012), 2357-2373

MSC (2010):
Primary 35B32, 35B40, 35B41, 37L30

DOI:
https://doi.org/10.1090/S0002-9939-2011-11071-2

Published electronically:
October 26, 2011

MathSciNet review:
2898698

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Abstract: The Chafee-Infante equation is one of the canonical infinite-dimensional dynamical systems for which a complete description of the global attractor is available. In this paper we study the structure of the pullback attractor for a non-autonomous version of this equation, , and investigate the bifurcations that this attractor undergoes as is varied. We are able to describe these in some detail, despite the fact that our model is truly non-autonomous; i.e., we do not restrict to `small perturbations' of the autonomous case.

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Additional Information

**A. N. Carvalho**

Affiliation:
Instituto de Ciências Matemáticas e de Computaçao, Universidade de São Paulo-Campus de São Carlos, Caixa Postal 668, 13560-970 São Carlos SP, Brazil

Email:
andcarva@icmc.usp.br

**J. A. Langa**

Affiliation:
Departamento de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160, 41080 Sevilla, Spain

Email:
langa@us.es

**J. C. Robinson**

Affiliation:
Mathematical Institute, University of Warwick, Coventry, CV4 7AL, United Kingdom

Email:
j.c.robinson@warwick.ac.uk

DOI:
https://doi.org/10.1090/S0002-9939-2011-11071-2

Received by editor(s):
September 14, 2010

Received by editor(s) in revised form:
February 15, 2011

Published electronically:
October 26, 2011

Additional Notes:
The first author was partially supported by CNPq 302022/2008-2, CAPES/DGU 267/2008 and FAPESP 2008/55516-3, Brazil

The second author was partially supported by Ministerio de Ciencia e Innovación grants #MTM2008-0088, #PBH2006-0003-PC, and Junta de Andalucía grants #P07-FQM-02468, #FQM314 and #HF2008-0039, Spain

The third author is currently an EPSRC Leadership Fellow, grant #EP/G007470/1.

Communicated by:
Yingfei Yi

Article copyright:
© Copyright 2011
American Mathematical Society