Exact renormalization group approach to a nonlinear diffusion equation

TL;DR

This paper applies the exact renormalization group to a nonlinear diffusion equation with discontinuous diffusion coefficients, deriving an anomalous diffusion exponent through a novel regularization scheme and perturbation analysis.

Contribution

It introduces a new regularization scheme and applies the exact renormalization group to derive the anomalous diffusion exponent for nonlinear diffusion equations.

Findings

Renormalization leads to an anomalous diffusion exponent

A new regularization scheme is proposed

Full-order perturbation series calculation achieved

Abstract

The exact renormalization group is applied to a nonlinear diffusion equation with a discontinuous diffusion coefficient. The generating functional of the solution for the initial-value problem of nonlinear diffusion equations is first introduced, and next a new regularization scheme is presented. It is shown that the renormalization of an action functional in the generating functional leads to an anomalous diffusion exponent in full order of the perturbation series with respect to a nonlinearity.