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

In this paper, we prove some asymptotic higher-order integrability for the solution of a semilinear reaction-diffusion equation defined on RN(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 (L2(RN),L2(RN)∩Lp(RN))-global attractor immediately; moreover, such an attractor can attract every L2(RN)-bounded set with the L2(RN)∩Lp+δ(RN)-norm for any δ∈[0,∞).