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arXiv · 0906.2206

Renormalization Group Analysis of Nonlinear Diffusion Equations with Periodic Coefficients

Gastao A. Braga·Frederico Furtado·Jussara M. Moreira·Leonardo T. Rolla
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Abstract

In this paper we present an efficient numerical approach based on the Renormalization Group method for the computation of self-similar dynamics. The latter arise, for instance, as the long-time asymptotic behavior of solutions to nonlinear parabolic partial differential equations. We illustrate the approach with the verification of a conjecture about the long-time behavior of solutions to a certain class of nonlinear diffusion equations with periodic coefficients. This conjecture is based on a mixed argument involving ideas from homogenization theory and the Renormalization Group method. Our numerical approach provides a detailed picture of the asymptotics, including the determination of the effective or renormalized diffusion coefficient.

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Gastao A. Braga, Frederico Furtado, Jussara M. Moreira, Leonardo T. Rolla. 2009-06-11. Renormalization Group Analysis of Nonlinear Diffusion Equations with Periodic Coefficients. https://arxiv.org/abs/0906.2206

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