Renormalization Group Analysis of Nonlinear Diffusion Equations with Time Dependent Coefficients and Marginal Perturbations |
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Authors: | Gastão A Braga Jussara M Moreira |
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Institution: | 1.Departamento de Matemática,Universidade Federal de Minas Gerais,Belo Horizonte,Brazil |
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Abstract: | 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. |
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