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Anomalous exponents and RG for nonlinear diffusion equations

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  • 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 $R^n$.
    Mathematics Subject Classification: Primary 35J55; Secondary 92D25.

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