Attractors for the semilinear reaction-diffusion equation with distribution derivatives

We investigate the asymptotic behavior of solutions to a nonlinear reaction-diffusion equation with distribution derivatives in the inhomogeneous term. Because the solutions of this equation are not very regular, i.e., u only belongs to L-p(R-n) boolean AND H-1(R-n), and u(t) is only in H-1(R-n) for the forcing term in H-1(R-n), the standard method does not directly work in our case. We demonstrate the asymptotic regularity of the solution to obtain the (L-2(R-n), H-1(R-n))-asymptotic compactness of the semigroup and therefore the existence of a (L-2(R-n), H-1(R-n))-global attractor. In particular cases, our results enable us to improve on some previously known results. (C) 2013 AIP Publishing LLC.