We study the long-time asymptotics of a certain class of nonlinear diffusion equations with time-dependent diffusion coefficients which arise, for instance, in the study of transport by randomly fluctuating velocity fields. Our primary goal is to understand the interplay between anomalous diffusion and nonlinearity in determining the long-time behavior of solutions. The analysis employs the renormalization group method to establish the self-similarity and to uncover universality in the way solutions decay to zero.
Discrete and Continuous Dynamical Systems-Series B
Braga, G. A.; Furtado, Fred; Moreira, J. M.; and Rolla, L. T. (2007). "Renormalization Group Analysis of Nonlinear Diffusion Equations with Time Dependent Coefficients: Analytical Results." Discrete and Continuous Dynamical Systems-Series B 7.4, 699-715.