Global attractors for a class of semilinear degenerate parabolic equations

摘要

In this paper, we consider the long-time behavior for a class of semi-linear degenerate parabolic equations with the nonlinearity?ff?satisfying the polynomial growth of arbitrary?p?1p?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?(L2(Ω),Lp(Ω))(L2(Ω),Lp(Ω))?-global attractors immediately; moreover, such an attractor can attract every bounded subset of?L2(Ω)L2(Ω)?with the?Lp+δLp+δ?-norm for any?δ∈[0,+∞)δ∈[0,+∞)?.