A solution decomposition for a singularly perturbed fourth-order problem

Katharina Höhne, Sebastian Franz, Marcus Waurick

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Abstract

We consider a singularly perturbed fourth-order problem with third-order terms on the unit square. With a formal power series approach, we decompose the solution into solutions of reduced (third-order) problems and various layer parts. The existence of unique solutions for the problem itself and for the reduced third-order problems is also addressed. To our knowledge, this paper is a first attempt for a solution decomposition of such problems.
Original languageEnglish
Pages (from-to)77-100
Number of pages24
JournalAnalysis
Volume37
Issue number2
Early online date30 May 2017
DOIs
Publication statusPublished - 1 Jun 2017

Keywords

  • asymptomatic expansion
  • singular perturbations
  • fourth-order problem
  • boundary layers

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