Notes on the Global Attractors for Semigroup

Lan Xu, Yuhua Shi

Department of Mathematics, Soochow University, Suzhou, China.
Suzhou Vocational University, Suzhou, China.

DOI: 10.4236/ijmnta.2013.24030                

Abstract

First we introduce two necessary and sufficient conditions which ensure the existence of the global attractors for semigroup. Then we recall the concept of measure of noncompactness of a set and recapitulate its basic properties. Finally, we prove that these two conditions are equivalent directly.

Keywords

Natural Global Attractors; Measure of Noncompactness; Asymptotic Compactness; w-Limit Compact

Conflicts of Interest

The authors declare no conflicts of interest.

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