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Uniform attractors for a non-autonomous parabolic equation involving Grushin operator. (English) Zbl 1227.35077

Summary: We consider the first initial boundary value problem for a non-autonomous semilinear degenerate parabolic equation involving the Grushin operator, in which the nonlinearity satisfies the polynomial condition of arbitrary order and the external force is normal. Using the asymptotic a priori estimate method, we prove the existence of uniform attractors for this problem. The obtained results, in particular, improve some recent ones for the non-autonomous Laplacian equation.

MSC:

35B41 Attractors
35K65 Degenerate parabolic equations
35K58 Semilinear parabolic equations
35K20 Initial-boundary value problems for second-order parabolic equations
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