Automatic Control and Computer Sciences

, Volume 51, Issue 7, pp 606–613 | Cite as

Asymptotics, Stability, and Region of Attraction of Periodic Solution to a Singularly Perturbed Parabolic Problem with Double Root of a Degenerate Equation

  • V. F. Butuzov
  • N. N. Nefedov
  • L. Recke
  • K. R. Schneider
Article

Abstract

For a singularly perturbed parabolic problem with Dirichlet boundary conditions, the asymptotic decomposition of a solution periodic in time and with boundary layers near the ends of the segment where the degenerate equation has a double root is constructed and substantiated. The construction algorithm for the asymptotics and the behavior of the solution in the boundary layers turn out to differ significantly as compared to the case of a simple root of a degenerate equation. The stability of the periodic solution and its region of attraction are also studied.

Keywords

singularly perturbed reaction–diffusion equations asymptotic approximations periodic solutions boundary layers Lyapunov stability region of attraction 

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Copyright information

© Allerton Press, Inc. 2017

Authors and Affiliations

  • V. F. Butuzov
    • 1
  • N. N. Nefedov
    • 1
  • L. Recke
    • 2
  • K. R. Schneider
    • 3
  1. 1.Lomonosov Moscow State UniversityMoscowRussia
  2. 2.Institut für MathematikHU BerlinBerlinGermany
  3. 3.Weierstrass Institute for Applied Analysis and StochasticsBerlinGermany

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