WIAS Preprint No. 1672, (2011)

On a singularly perturbed initial value problem in case of a double root of the degenerate equation



Authors

  • Butuzov, Valentin F.
  • Nefedov, Nikolai N.
  • Recke, Lutz
  • Schneider, Klaus

2010 Mathematics Subject Classification

  • 34A12 34E05 34E15

Keywords

  • singularly perturbed first order ordinary differential equation, initial value problem, boundary layer, double root of degenerate equation, asymptotic expansion

Abstract

We study the initial value problem of a singularly perturbed first order ordinary differential equation in case that the degenerate equation has a double root. We construct the formal asymptotic expansion of the solution such that the boundary layer functions decay exponentially. This requires a modification of the standard procedure. The asymptotic solution will be used to construct lower and upper solutions guaranteeing the existence of a unique solution and justifying its asymptotic expansion.

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