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

Technische Universität Dresden

Research output: Contribution to journal › Article › peer-review

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 (Germany)
Volume	37
Issue number	2
DOIs	https://doi.org/10.1515/anly-2016-0026
Publication status	Published - 1 Jun 2017

Keywords

Asymptotic expansion
boundary layers
fourth-order problem
singular perturbations

ASJC Scopus subject areas

Analysis
Numerical Analysis
Applied Mathematics

Access to Document

10.1515/anly-2016-0026

Cite this

@article{3564c55491d24e24a8361d7bfbb22c3b,

title = "A solution decomposition for a singularly perturbed fourth-order problem",

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.",

keywords = "Asymptotic expansion, boundary layers, fourth-order problem, singular perturbations",

author = "Katharina H{\"o}hne and Sebastian Franz and Marcus Waurick",

year = "2017",

month = jun,

day = "1",

doi = "10.1515/anly-2016-0026",

language = "English",

volume = "37",

pages = "77--100",

journal = "Analysis (Germany)",

issn = "0174-4747",

publisher = "Oldenbourg Verlag",

number = "2",

}

TY - JOUR

T1 - A solution decomposition for a singularly perturbed fourth-order problem

AU - Höhne, Katharina

AU - Franz, Sebastian

AU - Waurick, Marcus

PY - 2017/6/1

Y1 - 2017/6/1

N2 - 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.

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 - Asymptotic expansion

KW - boundary layers

KW - fourth-order problem

KW - singular perturbations

UR - http://www.scopus.com/inward/record.url?scp=85020470747&partnerID=8YFLogxK

UR - http://dx.doi.org/10.1515/anly-2016-0026

U2 - 10.1515/anly-2016-0026

DO - 10.1515/anly-2016-0026

M3 - Article

AN - SCOPUS:85020470747

SN - 0174-4747

VL - 37

SP - 77

EP - 100

JO - Analysis (Germany)

JF - Analysis (Germany)

IS - 2

ER -

A solution decomposition for a singularly perturbed fourth-order problem

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Mathematical Foundations of Metamaterials: Homogenisation, Dissipation and Operator Theory

Cite this

A solution decomposition for a singularly perturbed fourth-order problem

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Projects

Mathematical Foundations of Metamaterials: Homogenisation, Dissipation and Operator Theory

Cite this