Long-time behavior of reaction–diffusion equations with dynamical boundary condition

In this paper, we study the long-time behavior of the reaction–diffusion equation with dynamical boundary condition, where the nonlinear terms ff and gg satisfy the polynomial growth condition of arbitrary order. Some asymptotic regularity of the solution has been proved. As an application of the asymptotic regularity results, we can not only obtain the existence of a global attractor AA in (H1(Ω)∩Lp(Ω))×Lq(Γ)(H1(Ω)∩Lp(Ω))×Lq(Γ) immediately, but also can show further that AA attracts every L2(Ω)×L2(Γ)L2(Ω)×L2(Γ)-bounded subset with (H1(Ω)∩Lp+δ(Ω))×Lq+κ(Γ)(H1(Ω)∩Lp+δ(Ω))×Lq+κ(Γ)-norm for any δ,κ∈[0,∞)δ,κ∈[0,∞).