On pullback attractors in Lp for nonautonomous reaction-diffusion equations

Using the method introduced in Zhong et al. (2006) [17] together with a new way of dealing with well known estimates of solutions introduced in Lukaszewicz (in press) [9] we prove the existence of a unique minimal pullback attractor for the evolutionary process associated with a nonautonomous nonlinear reaction-diffusion system in L-p, p >= 2, in which the right hand side satisfies only a certain integrability condition. In particular, we generalize a result obtained recently in Li et al. (2009) [13] where an at most exponential growth of the right hand side has been assumed for times going to both plus and minus infinity. (C) 2010 Elsevier Ltd. All rights reserved.