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THE FILLED INELASTIC MEMBRANE: A SET OF CHALLENGING PROBLEMS IN THE CALCULUS OF VARIATIONS

Part of: Optimality conditions

Published online by Cambridge University Press:  02 July 2009

MICHAEL A. B. DEAKIN
MICHAEL A. B. DEAKIN*
Affiliation:
School of Mathematical Sciences, Monash University, VIC 3800, Australia (email: michael.deakin@sci.monash.edu.au)
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Abstract

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In a wide variety of related problems, a flexible but inextensible membrane is filled to capacity with incompressible fluid. In all such cases, the resulting shape satisfies a set of three simultaneous partial differential equations. At present there are no known solutions of any generality, and the main aim of this paper is to formulate the partial differential equations with a view to stimulating further interest in this important class of problems.

Keywords

constrained maximizationinelastic membrane

MSC classification

Secondary: 49K20: Problems involving partial differential equations

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 80 , Issue 3 , December 2009 , pp. 506 - 509
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2009

References

[1]Basinski, F., Qi, C. and Waldman, I., ‘Designing the shape of a large scientific balloon’, Appl. Math. Model. 25 (2001), 953–956.CrossRefGoogle Scholar
[2]Gammel, A., ‘The teabag constant’, http://www.dse.nl/∼andreas/teabag.html.Google Scholar
[3]Mladenov, I. M., ‘On the geometry of the Mylar balloon’, C.R. Acad. Bulgare Sci. 54(9) (2001), 39–44.Google Scholar
[4]Oprea, J., Differential Geometry and its Applications, 2nd edn (Mathematical Association of America, Washington, DC, 2007), pp. 371–380.CrossRefGoogle Scholar
[5]Paulsen, W. H., ‘What is the shape of a Mylar balloon?’, Amer. Math. Monthly 101(10) (1994), 953–958.CrossRefGoogle Scholar
[6]Robin, A. C., ‘Paper bag problem’, Math. Today (June 2004), 104–107.Google Scholar
[7] Wikipedia contributors, ‘Paper bag problem’, (Wikipedia, The Free Encyclopedia)http://en.wikipedia.org/w/index.php?title=Paper_bag_problem&oldid=236235050.Google Scholar