Xiang Li - Department of Mathematics and Systems Science, College of Science, National University of Defense Technology, Changsha, 410073, China (email)
Abstract: In this paper, we consider the long time behavior of a non-autonomous parabolic PDE with a discrete state-dependent delay. We study the existence of compact kernel sections and unique complete trajectory of the corresponding problem. Furthermore, we obtain the (almost) periodic solution which attracts all solutions provided the time dependent terms are (almost) periodic with respect to time $t$.
Keywords: State-dependent delay, kernel section, complete trajectory, periodic
solution, almost periodic solution.
Received: January 2010; Revised: October 2010; Published: December 2010.
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