WIAS Preprint No. 1683, (2012)

On existence and asymptotic stability of periodic solutions with an interior layer of reaction-advection-diffusion equations



Authors

  • Nefedov, Nikolai
  • Recke, Lutz
  • Schneider, Klaus

2010 Mathematics Subject Classification

  • 35B10 35B25 35B35 35C20 35K10

Keywords

  • singulary pertubed parabolic periodic problems, exponential asymptotic stability, Krein-Rutman theorem, lower and upper solutions

Abstract

We consider a singularly perturbed parabolic periodic boundary value problem for a reaction-advection-diffusion equation. We construct the interior layer type formal asymptotics and propose a modified procedure to get asymptotic lower and upper solutions. By using sufficiently precise lower and upper solutions, we prove the existence of a periodic solution with an interior layer and estimate the accuracy of its asymptotics. Moreover, we are able to establish the asymptotic stability of this solution with interior layer

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