Higher-order integrability for a semilinear reaction–diffusion equation with distribution derivatives in

In this paper, we prove some asymptotic higher-order integrability for the solution of a semilinear reaction–diffusion equation defined on R N ( N ⩾ 3 ) with a polynomially growing nonlinearity of arbitrary order and with distribution derivatives in the inhomogeneous term. As an application, we obtain the existence of a ( L 2 ( R N ) , L 2 ( R N ) ∩ L p ( R N ) ) -global attractor immediately; moreover, such an attractor can attract every L 2 ( R N ) -bounded set with the L 2 ( R N ) ∩ L p + δ ( R N ) -norm for any δ ∈ [ 0 , ∞ ) .