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June  2007, 6(2): 481-486. doi: 10.3934/cpaa.2007.6.481

A result on the existence of global attractors for semigroups of closed operators

V. Pata 1, and  Sergey Zelik 2,

1. 

Dipartimento di Matematica "F. Brioschi", Politecnico di Milano, I-20133 Milano
2. 

Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117 Berlin

Received  July 2006 Revised  December 2006 Published  March 2007

In this note, we establish a general result on the existence of global attractors for semigroups $S(t)$ of operators acting on a Banach space $\mathcal X$, where the strong continuity $S(t)\in C(\mathcal X,\mathcal X)$ is replaced by the much weaker requirement that $S(t)$ be a closed map.
Keywords: global attractors, Semigroups of operators, connected attractors., closed operators, abstract Cauchy problems.
Mathematics Subject Classification: Primary: 34D45; Secondary: 47H20, 47J3.
Citation: V. Pata, Sergey Zelik. A result on the existence of global attractors for semigroups of closed operators. Communications on Pure & Applied Analysis, 2007, 6 (2) : 481-486. doi: 10.3934/cpaa.2007.6.481
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