Intermediate asymptotics in L1 for general nonlinear diffusion equations

Relative entropy methods have received a lot of attention in the last few years not only in the context of linear parabolic equations [12,1] but also to handle nonlinear diffusion problems [11,5,7,4,9] and get decay estimates and asymptotic diffusion results. The goal of this letter is to give results on intermediate asymptotics for general nonlinearities. Here, we are not concerned with existence questions (see for instance [4] for a discussion); in all what follows we will assume that the solutions are such that the entropy function and its first derivative are well defined. Consider a solution u ∈ C0(IR, L+(IR )) of ut = ∆f(u) , (1)