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

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

2005-12-19

arxiv.org/abs/math/0512450v2

Discrete and Continuous Dynamical Systems. Series B, v. 7, p. 699-715, 2007

Mathematics

Analysis of PDEs

Includes referees' suggestions. 27 pages. No figures

Scientific paper

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.

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