Attractors for a Semilinear Parabolic System Involving the Grushin Operator
Considered here is the first initial boundary value problem for a semilinear degenerate
parabolic system involving the Grushin operator. We prove the existence of a finite-dimensional
global attractor in (L2(
))m for the semigroup associated to the problem in the general case. When
the system has a gradient structure, the global attractor is shown to be more regular by using the
so-called asymptotic a priori estimate method.