Pullback attractors for the non-autonomous reaction-diffusion equations in RN

In this paper, we prove the existence of the pullback attractors in L-2 (R-N), L-p (R-N), and H-1 (R-N) for a nonlinear reaction-diffusion equation in unbounded domains, in which the nonlinearity f satisfies the polynomial growth of arbitrary order p - 1(p > 2) and the external forcing g is an element of L-loc(2) (R; L-2 (R-N)) only subjects to the weaker integrability condition integral(t)(-infinity) e(alpha s)parallel to g(s)parallel to(2)(2)ds. Published under license by AIP Publishing.