Global attractors for a class of semilinear degenerate parabolic equations

In this paper, we consider the long-time behavior for a class of semi-linear degenerate parabolic equations with the nonlinearity f satisfying the polynomial growth of arbitrary p - 1 order. We establish some new estimates, i.e., asymptotic higher-order integrability for the difference of the solutions near the initial time. As an application, we obtain the (L-2(Omega), L-p(Omega))-global attractors immediately; moreover, such an attractor can attract every bounded subset of L-2(Omega) with the Lp+delta-norm for any delta is an element of [0, +infinity).