Anomalous exponents and RG for nonlinear diffusion equations

Yuanwei Qi

doi:10.3934/proc.2005.2005.738

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2005, Volume 2005: 738-745. Doi: 10.3934/proc.2005.2005.738 open access

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Anomalous exponents and RG for nonlinear diffusion equations

Yuanwei Qi^1,

1.
Department of Mathematics, University of Central Florida, Orlando, Fl 32816

Received: September 2004

Revised: May 2005

Published: August 2005

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Abstract

In this paper, we discuss how to combine Renormalization Group Methods (RG) and classical PDE techniques to study nonlinear diffusion equations and systems with critical nonlinearity. In particular, we demonstrate, using several examples, the successful application of RG, when sharp a priori estimates are derived, in showing universal global dynamics involving anomalous exponents for nonlinear systems in $R^n$.

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Mathematics Subject Classification: Primary 35J55; Secondary 92D25.

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