On pullback attractors in LpLp 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 Łukaszewicz (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 LpLp, p≥2p≥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.