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Renormalization Group Analysis of Nonlinear Diffusion Equations with Periodic Coefficients

journal contribution
posted on 01.01.2003, 00:00 by G. A. Braga, Fred Furtado, J. M. Moreira, L. T. Rolla
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.

History

ISO

eng

Language

English

Publisher

University of Wyoming. Libraries

Journal title

Multiscale Modeling & Simulation

Collection

Faculty Publication - Department of Mathmatics & Statistics