Inverse problems theme year 2003-2004   

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.


  1. Basic ideas. Regular and singular perturbations: examples. Singularly perturbed (s.p.) ordinary differential equations: Tikhonov's theorem, asymptotic algorithm for initial value problems.
  2. Critical case for s.p. ordinary differential equations. Applications in chemical and biological kinetics: Michaelis-Menten system; three-molecular reactions.
  3. Boundary value problems for s.p. ordinary differential equations. Asymptotic algorithm and special cases: boundary layers, internal layers, spikes.
  4. 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.
  5. If time permits: S.p. problems of current interest (models reduction for large systems, problems with exchange of stabilities, etc.).


Mon 14.4.Tue 15.4.Wed 16.4.
10.15 - 11.00Hall EHall EHall E
11.15 - 12.00Hall EHall EHall E
12.15 - 13.00
13.15 - 14.00Hall BHall EHall 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 start-up for the Inverse Problems theme year 2003-2004 organized by the Finnish Inverse Problems Society and the Finnish Mathematical Society.

Kenrick Bingham
8 Apr 2003
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