Journal
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
Volume 34, Issue 10, Pages 4155-4182Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/dcds.2014.34.4155
Keywords
Reaction-diffusion equations; set-valued dynamical system; global attractor; unstable manifolds; asymptotic behaviour
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Funding
- spanish Ministerio de Ciencia e Innovacion
- FEDER [MTM2011-22411, MTM2012-31698]
- Ukrainian State Fund for Fundamental Researches [GP/F44/076, GP/F49/070]
- National Academy of Sciences of Ukraine [2273/13]
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In this paper we study the structure of the global attractor for a reaction-diffusion equation in which uniqueness of the Cauchy problem is not guarantied. We prove that the global attractor can be characterized using either the unstable manifold of the set of stationary points or the stable one but considering in this last case only solutions in the set of bounded complete trajectories.
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