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Renormalization Group Analysis of Nonlinear Diffusion Equations with Periodic Coefficients
Braga, G. A. Furtado, Fred Moreira, J. M. Rolla, L. T.
Braga, G. A.
Furtado, Fred
Moreira, J. M.
Rolla, L. T.
Abstract
Description
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.
Date
2003-01-01
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Publisher
University of Wyoming. Libraries
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Keywords
renormalization group,partial differential equations,multiple scale problems,asymptotic behavior,Mathematics