WIAS Report No. 21, (2002)

Singularly Perturbed Problems in Case of Exchange of Stabilities


  • Butuzov, Valentin F.
  • Nefedov, Nikolai N.
  • Schneider, Klaus R.

2010 Mathematics Subject Classification

  • 34-02 35-02 34E15 34E05 34A12 34B15 35B25 35J25 35K57


  • singularly perturbed differential equations, asymptotic expansions, exchange of stabilities, delayed exchange of stabilities, initial value problems, boundary value problems, initial-boundary value problems




This report is devoted to a class of singularly perturbed differential equations which cannot be treated in the frame of the standard theory of singularly perturbed problems for ordinary as well as for partial differential equations. This new class of problems is called as it singularly perturbed problems in case of exchange of stabilities. The main results are concerned with the asymptotic behavior of the solutions of initial value, boundary value and initial-boundary value problems as the perturbation parameter tends to zero. The report is based essentially on papers of the authors and their colleagues published in the last six to seven years in the frame of cooperation between the Department of Mathematics of the Faculty of Physics of the Lomonosov Moscow State University and the Department of Dynamical Systems of the Weierstrass Institute for Applied Analysis and Stochastics in Berlin.