Structure and bifurcation of pullback attractors in a non-autonomous Chafee-Infante equation
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- by A. N. Carvalho, J. A. Langa and J. C. Robinson PDF
- Proc. Amer. Math. Soc. 140 (2012), 2357-2373 Request permission
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.References
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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
- 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
- © Copyright 2011 American Mathematical Society
- 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
- MathSciNet review: 2898698