Attractors for the semilinear reaction-diffusion equation with distribution derivatives in unbounded domains

In this paper, we prove the existence of global attractors for a nonlinear reaction-diffusion equation with a nonlinearity having a polynomial growth of arbitrary order p-1(p⩾2), and with distribution derivatives in the inhomogeneous term. The global attractors are obtained in L2(Rn) and Lp(Rn), respectively. A new a priori estimate method has been used. Since the solutions of the equation have no higher regularity and the semigroup associated with the solutions is not continuous in Lp(Rn), the results are new and appear to be optimal.