A transform method for the biharmonic equation in multiply connected circular domains

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Title: A transform method for the biharmonic equation in multiply connected circular domains
Authors: Luca, E
Crowdy, DG
Item Type: Journal Article
Abstract: A new transform approach for solving mixed boundary value problems for the biharmonic equation in simply and multiply connected circular domains is presented. This work is a sequel to Crowdy (2015, IMA J. Appl. Math., 80, 1902–1931) where new transform techniques were developed for boundary value problems for Laplace’s equation in circular domains. A circular domain is defined to be a domain, which can be simply or multiply connected, having boundaries that are a union of circular arc segments. The method provides a flexible approach to finding quasi-analytical solutions to a wide range of problems in fluid dynamics and plane elasticity. Three example problems involving slow viscous flows are solved in detail to illustrate how to apply the method; these concern flow towards a semicircular ridge, a translating and rotating cylinder near a wall as well as in a channel geometry.
Issue Date: 27-Nov-2018
Date of Acceptance: 8-Jun-2018
URI: http://hdl.handle.net/10044/1/62161
DOI: https://dx.doi.org/10.1093/imamat/hxy030
ISSN: 0272-4960
Publisher: Oxford University Press (OUP)
Start Page: 942
End Page: 976
Journal / Book Title: IMA Journal of Applied Mathematics
Volume: 83
Issue: 6
Copyright Statement: © The Author(s) 2018. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved. This is a pre-copy-editing, author-produced version of an article accepted for publication in IMA Journal of Applied Mathematics following peer review.
Sponsor/Funder: The Leverhulme Trust
Engineering & Physical Science Research Council (EPSRC)
The Royal Society
Funder's Grant Number: RPG-358
EP/K019430/1
WM120037
Keywords: Science & Technology
Physical Sciences
Mathematics, Applied
Mathematics
biharmonic equation
transform method
mixed boundary value problem
circular domain
STOKES-FLOW
LAPLACES-EQUATION
VISCOUS-FLUID
SHEAR-FLOW
CYLINDER
PLANE
SEPARATION
MOTION
0102 Applied Mathematics
Applied Mathematics
Publication Status: Published
Online Publication Date: 2018-07-06
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences



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