Selection, Stability and Renormalization

TL;DR

This paper extends the concept of structural stability to front propagation speed selection, using renormalization group methods to unify singular perturbations and amplitude equations as renormalization group equations.

Contribution

It introduces a novel application of renormalization group techniques to stability and speed selection in front propagation problems.

Findings

Singular perturbations are best understood as renormalized perturbation methods.

Amplitude equations are equivalent to renormalization group equations.

Provides a unified framework for stability analysis in applied mathematics.

Abstract

We illustrate how to extend the concept of structural stability through applying it to the front propagation speed selection problem. This consideration leads us to a renormalization group study of the problem. The study illustrates two very general conclusions: (1) singular perturbations in applied mathematics are best understood as renormalized perturbation methods, and (2) amplitude equations are renormalization group equations.