Renormalization group analysis of nonlinear diffusion equations with time dependent coefficients: Analytical results
Gastão A. Braga, Frederico Furtado, Jussara M. Moreira, Leonardo T. Rolla · Discrete and Continuous Dynamical Systems - B · 2007
We study the long-time asymptotics of a certain class of nonlineardiffusion equations with time-dependent diffusion coefficients whicharise, for instance, in the study of transport by randomlyfluctuating velocity fields. Our primary goal is to understand theinterplay between anomalous diffusion and nonlinearity indetermining the long-time behavior of solutions. The analysisemploys the renormalization group method to establish theself-similarity and to uncover universality in the way solutionsdecay to zero.