A solution decomposition for a singularly perturbed fourth-order problem

Katharina Höhne, Sebastian Franz, Marcus Waurick

Research output: Contribution to journalArticle

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 (Germany)
Volume37
Issue number2
DOIs
Publication statusPublished - 1 Jun 2017

Fingerprint

Singularly Perturbed
Fourth Order
Decomposition
Decompose
Formal Power Series
Unique Solution
Unit
Term

Keywords

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

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Applied Mathematics

Cite this

A solution decomposition for a singularly perturbed fourth-order problem. / Höhne, Katharina; Franz, Sebastian; Waurick, Marcus.

In: Analysis (Germany), Vol. 37, No. 2, 01.06.2017, p. 77-100.

Research output: Contribution to journalArticle

Höhne, Katharina ; Franz, Sebastian ; Waurick, Marcus. / A solution decomposition for a singularly perturbed fourth-order problem. In: Analysis (Germany). 2017 ; Vol. 37, No. 2. pp. 77-100.
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