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## 学术活动

Some discussions on existence of global attractors for operator semigroups on metric spaces

Inthis talk,  we  discuss the existence of global attractorsfor  continuous operator semigroups incomplete metric spaces.  As a result, weshow a  new characterization of theexistence of global attractors for continuous semigroups in complete metricspaces in terms of measure of noncompactness. In particular, we present asufficient and necessary condition of the existence of global attractors forcontinuous operator semigroups in $L^p$-spaces for $0<p<\infty$, whichcan be understood as an  improvement ofsome  known theorems. Applying thesetheorems,  we give a short andself-contained proof of a classical result related to the existence of globalattractors of a class of reaction-diffusion equations.

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