Kernel sections and (almost) periodic solutions of a non-autonomous parabolic PDE with a discrete state-dependent delay

Pages: 687 - 700, Volume 10, Issue 2, March 2011

doi:10.3934/cpaa.2011.10.687       Abstract        References        Full Text (358.3K)       Related Articles

Xiang Li - Department of Mathematics and Systems Science, College of Science, National University of Defense Technology, Changsha, 410073, China (email)
Zhixiang 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.
Mathematics Subject Classification:  34K13, 35K90.

Received: January 2010;      Revised: October 2010;      Published: December 2010.

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