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