Renormalization Group Analysis of Nonlinear Diffusion Equations with Periodic Coefficients

Details Renormalization Group Analysis of Nonlinear Diffusion Equations with Periodic Coefficients Renormalization Group Analysis of Nonlinear Diffusion Equations with Periodic Coefficients

2009-06-11

arxiv.org/abs/0906.2206v1

Multiscale Model. Simul. 1 (2003), p. 630-644

Mathematics

Analysis of PDEs

19 pages, including 13 figures. Typeset with LaTeX

Scientific paper

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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