**On the Global Attractor for a Semilinear Strongly Degenerate Parabolic Equation **

* Mai Xuan Thao *

**Abstract**

We prove the existence of a global attractor in *L* ^{2}(Ω). This global attractor is then shown to have a finite fractal dimension in *L* ^{2}(Ω). We also study the existence and exponential stability of the unique stationary solution to the problem.