Attractors for parabolic equations related to Caffarelli-Kohn-Nirenberg inequalities
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
Boundary Value Problems 2012, 2012:35 doi:10.1186/1687-2770-2012-35Published: 28 March 2012
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.