Open Access Review

Attractors for parabolic equations related to Caffarelli-Kohn-Nirenberg inequalities

Nguyen Dinh Binh1* and Cung The Anh2

Author Affiliations

1 Department of Applied Mathematics and Informatics, Hanoi University of Science and Technology, 1 Dai Co Viet, Hai Ba Trung, Hanoi, Vietnam

2 Department of Mathematics, Hanoi National University of Education, 136 Xuan Thuy, Cau Giay, Hanoi, Vietnam

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Boundary Value Problems 2012, 2012:35  doi:10.1186/1687-2770-2012-35

Published: 28 March 2012

Abstract

Using the theory of uniform global attractors for multi-valued semiprocesses, we prove the existence of attractors for quasilinear parabolic equations related to Caffarelli-Kohn- Nirenberg inequalities, in which the conditions imposed on the nonlinearity provide the global existence of weak solutions but not uniqueness, in both autonomous and non-autonomous cases.

Mathematics Subject Classification 2010: 35B41, 35K65, 35D30.

Keywords:
Caffarelli-Kohn-Nirenberg inequalities; non-uniqueness; weak solution; multivalued semiflow; multi-valued semiprocess; compact attractor; compactness and monotonicity methods