Inverse problems theme year 20032004
Introduction to Asymptotic Methods for Differential Equations
(The Boundary Function Method)
Minicourse by
Professor
Leonid V. Kalachev
University of Montana
Monday, 14 April to Wednesday, 16 April, 2003,
at the Institute of Mathematics
of Helsinki University of Technology
One study credit (opintoviikko) will be given to those who
solve a set of exercises and turn them in.
Content

Basic ideas. Regular and singular perturbations: examples. Singularly
perturbed (s.p.) ordinary differential equations: Tikhonov's theorem,
asymptotic algorithm for initial value problems.

Critical case for s.p. ordinary differential equations. Applications
in chemical and biological kinetics: MichaelisMenten system;
threemolecular reactions.

Boundary value problems for s.p. ordinary differential equations. Asymptotic algorithm and special cases: boundary layers, internal layers, spikes.

Boundary value problems for s.p. partial differential
equations. Method of Vishik and Lyusternik. Corner boundary functions;
problems with fast diffusion; critical case for partial differential
equations.
 If time permits: S.p. problems of current interest (models
reduction for large systems, problems with exchange of stabilities, etc.).
Schedule
 Mon 14.4.  Tue 15.4.  Wed 16.4. 
10.15  11.00  Hall E  Hall E  Hall E 
11.15  12.00  Hall E  Hall E  Hall E 
12.15  13.00  
13.15  14.00  Hall B  Hall E  Hall E 
Halls B and E are in the main building of HUT near the main entrance.
HUT is located in
Otaniemi
in the Helsinki area.
The lectures constitute an early startup for the
Inverse Problems
theme year 20032004
organized by the
Finnish Inverse Problems
Society
and the
Finnish Mathematical Society.