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

V. Pata; Sergey Zelik

doi:10.3934/cpaa.2007.6.481

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2007, Volume 6, Issue 2: 481-486. Doi: 10.3934/cpaa.2007.6.481

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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: June 30, 2006

Revised: November 30, 2006

Published: May 2007

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Abstract

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.

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Mathematics Subject Classification: Primary: 34D45; Secondary: 47H20, 47J35.

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