Title: On uniform global attractors for a class of non-autonomous degenerate parabolic equations

Authors: Cung The Anh; Nguyen Dinh Binh; Le Thi Thuy

Addresses: Department of Mathematics, Hanoi National University of Education, 136 Xuan Thuy, Cau Giay, Hanoi, Vietnam. ' Faculty of Applied Mathematics and Informatics, Hanoi University of Science and Technology, 1 Dai Co Viet, Hai Ba Trung, Hanoi, Vietnam. ' Department of Mathematics, Electric Power University, 235, Hoang Quoc Viet, Tu Liem, Hanoi, Vietnam

Abstract: Using the theory of Multivalued Semiprocesses (MSPs) of Melnik and Valero, we prove the existence of a uniform global attractor for a non-autonomous quasilinear degenerate parabolic equation in which the conditions imposed on the nonlinearity provide the global existence of a weak solution, but not uniqueness. In the semilinear case, we prove the Kneser property holds for solutions, and as a result we obtain the connectedness of the uniform global attractor. We also study the regularity of the uniform attractor in this case under some additional restrictions of the nonlinearity and the external force.

Keywords: non-autonomous degenerate parabolic equations; MSP; multivalued semiprocesses; uniform global attractors; Kneser property; compactness method; asymptotic a priori estimation.

DOI: 10.1504/IJDSDE.2012.045993

International Journal of Dynamical Systems and Differential Equations, 2012 Vol.4 No.1/2, pp.35 - 55

Available online: 19 Mar 2012 *

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