Electronic Journal of Differential Equations, Vol. 2009(2009), No. 61, pp. 1-13. Title: Existence and continuity of global attractors for a degenerate semilinear parabolic equation Authors: Cung The Anh (Hanoi National Univ. of Education, Vietnam) Tran Dinh Ke (Hanoi National Univ. of Education, Vietnam) Abstract: In this article, we study the existence and the upper semicontinuity with respect to the nonlinearity and the shape of the domain of global attractors for a semilinear degenerate parabolic equation involving the Grushin operator. Submitted December 20, 2008. Published May 04, 2009. Math Subject Classifications: 35B41, 35K65, 35D05. Key Words: Semilinear degenerate parabolic equation; Grushin operator; global solution; global attractor; upper semicontinuity; nonlinearity; shape of domain.