Electron. J. Diff. Equ., Vol. 2010(2010), No. 11, pp. 1-14.

Pullback attractors for non-autonomous parabolic equations involving Grushin operators

Cung The Anh

Using the asymptotic a priori estimate method, we prove the existence of pullback attractors for a non-autonomous semilinear degenerate parabolic equation involving the Grushin operator in a bounded domain. We assume a polynomial type growth on the nonlinearity, and an exponential growth on the external force. The obtained results extend some existing results for non-autonomous reaction-diffusion equations.

Submitted June 8, 2009. Published January 18, 2010.
Math Subject Classifications: 35B41, 35K65, 35D05.
Key Words: Non-autonomous degenerate equation; Grushin operator; global solution; pullback attractor; compactness method; asymptotic a priori estimate method.

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Cung The Anh
Department of Mathematics, Hanoi National University of Education
136 Xuan Thuy, Cau Giay, Hanoi, Vietnam
email: anhctmath@hnue.edu.vn

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