June  2007, 7(4): 699-715. doi: 10.3934/dcdsb.2007.7.699

Renormalization group analysis of nonlinear diffusion equations with time dependent coefficients: Analytical results

1. 

Departamento de Matemática, Universidade Federal de Minas Gerais, Caixa Postal 1621, Belo Horizonte, 30161-970, Brazil

2. 

Department of Mathematics, University of Wyoming, Laramie, 82071

3. 

Departamento de Matemática, Universidade Federal de Minas Gerais, Caixa Postal 1621, Beloa Horizonte, 30161-970, Brazil

4. 

Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina 110, Rio de Janeiro, 22460-320, Brazil

Received  December 2005 Revised  November 2006 Published  March 2007

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.
Citation: G. A. Braga, Frederico Furtado, Jussara M. Moreira, Leonardo T. Rolla. Renormalization group analysis of nonlinear diffusion equations with time dependent coefficients: Analytical results. Discrete & Continuous Dynamical Systems - B, 2007, 7 (4) : 699-715. doi: 10.3934/dcdsb.2007.7.699
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