Pullback attractors of non-autonomous reaction–diffusion equations in [formula omitted

Abstract

Using a method based on the concept of the Kuratowski measure of noncompactness of a bounded set as well as some new estimates of the solutions we prove the existence of a unique minimal pullback attractor in H 0 1 ( Ω ) for the process associated with non-autonomous reaction–diffusion equation without any restriction on the growing order of nonlinear terms ( p > 2 is arbitrary). In addition, the external forces g ( t ) satisfy only the weaker integrability condition than in the earlier similar research of Song and Wu (2007) [25] and Li et al. (2009) [18].