Acta Mathematica Vietnamica
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UNIFORM ATTRACTORS FOR A NON-AUTONOMOUS PARABOLIC EQUATION INVOLVING GRUSHIN OPERATOR
CUNG THE ANH, NGUYEN VAN QUANGpp. 19-33
Abstract
In this paper, 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.