FACW_MATH_2003_15403467_Braga_Furtado_Moreira_Rolla.pdf (280.53 kB)
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Renormalization Group Analysis of Nonlinear Diffusion Equations with Periodic Coefficients

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journal contribution
posted on 15.11.2021, 21:40 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.







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Multiscale Modeling & Simulation


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