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December  2009, 25(4): 1209-1217. doi: 10.3934/dcds.2009.25.1209

On the regularity of global attractors

Monica Conti 1, and  Vittorino Pata 1,

1. 

Politecnico di Milano - Dipartimento di Matematica "F. Brioschi", Via Bonardi 9, 20133 Milano

Received  January 2009 Revised  June 2009 Published  September 2009

This note is focused on a novel technique to establish the boundedness in more regular spaces for global attractors of dissipative dynamical systems, without appealing to uniform-in-time estimates. As an application, we consider the semigroup generated by the strongly damped wave equation with critical nonlinearity, whose attractor is shown to possess the optimal regularity.
Keywords: regularity, global attractor, absorbing set, semigroup, strongly damped wave equation., Solution operator.
Mathematics Subject Classification: Primary: 34D45, 47H20; Secondary: 35B33, 35L0.
Citation: Monica Conti, Vittorino Pata. On the regularity of global attractors. Discrete & Continuous Dynamical Systems, 2009, 25 (4) : 1209-1217. doi: 10.3934/dcds.2009.25.1209
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