International Journal of Differential Equations
Volume 2010 (2010), Article ID 103510, 17 pages
doi:10.1155/2010/103510
Research Article

Attractors for Nonautonomous Parabolic Equations without Uniqueness

Cung The Anh1 and Nguyen Dinh Binh2

1Department of Mathematics, Hanoi National University of Education, 136 Xuan Thuy, Cau Giay, 10307 Hanoi, Vietnam
2Department of Applied Mathematics and Informatics, Hanoi University of Technology, 1 Dai Co Viet, Hai Ba Trung, 10408 Hanoi, Vietnam

Received 9 September 2009; Revised 12 February 2010; Accepted 8 April 2010

Academic Editor: Igor D. Chueshov

Copyright © 2010 Cung The Anh and Nguyen Dinh Binh. 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.

Abstract

Using the theory of uniform global attractors of multivalued semiprocesses, we prove the existence of a uniform global attractor for a nonautonomous semilinear degenerate parabolic equation in which the conditions imposed on the nonlinearity provide the global existence of a weak solution, but not uniqueness. The Kneser property of solutions is also studied, and as a result we obtain the connectedness of the uniform global attractor.