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The Scientific World Journal
Volume 2016, Article ID 1871602, 9 pages
Research Article

The Existence of Weak -Pullback Exponential Attractor for Nonautonomous Dynamical System

School of Mathematics, Lanzhou City University, Lanzhou 730070, China

Received 5 January 2016; Accepted 22 February 2016

Academic Editor: Tuncay Candan

Copyright © 2016 Yongjun Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


First, for a process , we introduce a new concept, called the weak -pullback exponential attractor, which is a family of sets , for any , satisfying the following: (i) is compact, (ii) is positively invariant, that is, , and (iii) there exist such that ; that is, pullback exponential attracts . Then we give a method to obtain the existence of weak -pullback exponential attractors for a process. As an application, we obtain the existence of weak -pullback exponential attractor for reaction diffusion equation in with exponential growth of the external force.