Renormalization Group Analysis of Nonlinear Diffusion Equations with Periodic Coefficients
Analysis of PDEs
2016-09-06 v2 Numerical Analysis
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.
Cite
@article{arxiv.0906.2206,
title = {Renormalization Group Analysis of Nonlinear Diffusion Equations with Periodic Coefficients},
author = {Gastao A. Braga and Frederico Furtado and Jussara M. Moreira and Leonardo T. Rolla},
journal= {arXiv preprint arXiv:0906.2206},
year = {2016}
}