Journal of Statistical Physics

, Volume 148, Issue 2, pp 280–295 | Cite as

Renormalization Group Analysis of Nonlinear Diffusion Equations with Time Dependent Coefficients and Marginal Perturbations



In this paper we use a Renormalization Group (RG) method to study the long-time asymptotics of nonlinear diffusion equations with time-dependent diffusion coefficients and nonlinearities which are marginal (or critical) with respect to the RG operator. These equations describe the time evolution of the average concentration of a passive scalar being advected by a random velocity field. We prove that, besides the expected diffusive behavior, there is an extra logarithmic correction which is the imprint of the critical nonlinearity.


Renormalization group Partial differential equations Multiple scale Asymptotic behavior 



The authors wish to thank the precious discussions with Paulo Cesar Carrião on topics related to this paper.


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© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Departamento de MatemáticaUniversidade Federal de Minas GeraisBelo HorizonteBrazil

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