Renormalization Group Analysis of Nonlinear Diffusion Equations With Time Dependent Coefficients: Analytical Results

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...

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Bibliographic Details
Published in:arXiv.org 2016-09
Main Authors: Braga, Gastão A, Furtado, Frederico, Moreira, Jussara M, Rolla, Leonardo T
Format: Article
Language:English
Subjects:
Diffusion
Mathematical analysis
Nonlinear analysis
Nonlinear equations
Nonlinearity
Self-similarity
Time dependence
Variations
Velocity distribution
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Summary: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.
ISSN:2331-8422