PHYSICAL MATHEMATICS SEMINAR

TITLE:	RENORMALIZATION GROUP APPROACH TO 
	GLOBAL ASYMPTOTIC ANALYSIS


SPEAKER:	NIGEL GOLDENFELD
		Department of Physics
		University of Illinois at Urbana-Champaign

ABSTRACT: 

Renormalization and the renormalization group (RG) were originally
developed by physicists attempting to understand the divergent terms 
in perturbation theory, and the short distance behavior of quantum 
electrodynamics. During the last few years, these methods have been 
used to study the divergent terms in perturbation theory and the long 
time behavior of a variety of nonlinear partial differential equations. 
Problems studied include similarity solutions, especially intermediate 
asymptotics of the second kind (Barenblatt classification), and traveling 
waves. Examples include: porous medium equation, propagation of 
turbulence, and the Fisher-Kolmogorov-Petrovsky-Piskunov equation.
Most recently, singular perturbation problems for nonlinear differential 
equations have been treated with particular attention paid to multiple-scale 
analysis, boundary layers and WKB, and matched asymptotics.
The RG method starts from a regular perturbation expansion in the small 
parameter, and automatically generates an asymptotic sequence without 
requiring the user to make insightful guesses as to the presence of 
"unexpected" powers, logarithms, etc. The RG-generated uniform
approximation is practically more useful than that generated by matched 
asymptotics, even when extended to values of the small parameter of order 
unity.


TUESDAY, DECEMBER 9, 2003, 2:30 pm, Building 2, Room 338

Refreshments will be served at 3:30 PM in Room 2-349

Massachusetts Institute of Technology, Department of Mathematics, 
Cambridge, MA  02139