Asymptotic behaviour of nonlocal p-Laplacian reaction-diffusion problems

In this paper, we focus on studying the existence of attractors in the phase spaces L2(Ω) and Lp(Ω) (among others) for time-dependent p-Laplacian equations with nonlocal diffusion and nonlinearities of reaction-diffusion type. Firstly, we prove the existence of weak solutions making use of a change of variable which allows us to get rid of the nonlocal operator in the diffusion term. Thereupon, the regularising effect of the equation is shown applying an argument of a posteriori regularity, since under the assumptions made we cannot guarantee the uniqueness of weak solutions. In addition, this argument allows to ensure the existence of an absorbing family in W01,p(Ω). This leads to the existence of the minimal pullback attractors in L2(Ω), Lp(Ω) and some other spaces as Lp⁎−ϵ(Ω). Relationships between these families are also established.