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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

   

 

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
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, $ u_t=u_{xx}+\lambda u-\beta (t)u^3$, and investigate the bifurcations that this attractor undergoes as $ \lambda $ 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: http://dx.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



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