Selection, Stability and Renormalization

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.Comment: 38 pages, LaTeX, two PostScript figures available by anonymous ftp to gijoe.mrl.uiuc.edu (128.174.119.153) files /pub/front_kkfest_fig