Scaling, selfsimilarity and intermediate asymptotics
Math 488 Sec. G1
Spring 2001
Basic Information
 Instructor: Richard Laugesen
 email:laugesen@illinois.edu
 Homepage:
www.math.uiuc.edu/~laugesen
 Office: 376 Altgeld Hall
Phone: 3331329
 Class meets: Probably MWF at 3 pm, but that might
be flexible
 Room: Altgeld 441
Course outline
This is a "topics" course in applied mathematics. We aim for
a working knowledge of similarity and asymptotic methods
that will be useful for the future research of students in the class.
We will attempt to digest G. I. Barenblatt's book
"Scaling, selfsimilarity and intermediate asymptotics"
(Cambridge Texts in Applied Mathematics 14, 1996).
There will be only occasional homework. Students will make final
presentations, hopefully on papers from the similarity literature.
Prerequisites: classical ordinary and partial differential equations.
For example, Math 444 should provide plenty of background. But you
also need a love of calculus and applications!
We plan to cover the following topics:
 Dimensions, dimensional analysis and similarity

Selfsimilar solutions of the first and second kinds

Classification of similarity solutions
 Scaling and transformation groups, renormalization group
 Traveling waves
 Stability of selfsimilar solutions
 Scaling in turbulence
 Whatever else interests us, e.g. papers from the recent literature
And I'll try to arrange some guest lectures from workers in the field.
Application areas we will encounter include: heat flow, nuclear
explosions, fluid flow, filtration, shock waves, flame fronts,
and fracture of solids. No prior knowledge of those areas is needed. We
will just dive in and see what we can learn.
If you have any questions or concerns,
please contact me by email at laugesen@illinois.edu.
 Richard Laugesen