Necessary and sufficient conditions for the existence of time-dependent global attractor and application

摘要

In this paper, we are concerned with infinite dimensional dynamical systems in timedependent space. First, we characterize some necessary and sufficient conditions for the existence of the time-dependent global attractor by using a measure of noncompactness. Then, we give a new method to verify the sufficient condition. As a simple application, we prove the existence of the time-dependent global attractor for the damped equation in strong topological space. Published by AIP Publishing.