Anomalous exponents and RG for nonlinear diffusion equations

Pages: 738 - 745, Issue Special, August 2005

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Yuanwei Qi - Department of Mathematics, University of Central Florida, Orlando, Fl 32816, United States (email)

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 $R^n$.

Keywords:  Renormlization, Critical Nonlinearity, Anomalous Exponent.
Mathematics Subject Classification:  Primary 35J55; Secondary 92D25.

Received: September 2004;      Revised: May 2005;      Published: September 2005.