A solution decomposition for a singularly perturbed fourth-order problem

Katharina Höhne; Sebastian Franz; Marcus Waurick

doi:10.1515/anly-2016-0026

A solution decomposition for a singularly perturbed fourth-order problem

Katharina Höhne, Sebastian Franz, Marcus Waurick

Mathematics And Statistics

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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 language	English
Pages (from-to)	77-100
Number of pages	24
Journal	Analysis
Volume	37
Issue number	2
Early online date	30 May 2017
DOIs	https://doi.org/10.1515/anly-2016-0026
Publication status	Published - 1 Jun 2017

Keywords

asymptomatic expansion
singular perturbations
fourth-order problem
boundary layers

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10.1515/anly-2016-0026

Franz-etal-Analysis-2017-A-solution-decomposition-for-a-singularly-perturbedAccepted author manuscript, 249 KB

https://arxiv.org/pdf/1511.05378.pdfLicence: Unspecified

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AB - 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.

KW - asymptomatic expansion

KW - singular perturbations

KW - fourth-order problem

KW - boundary layers

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A solution decomposition for a singularly perturbed fourth-order problem

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