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Variational Calculus Involving Singular Integral Equations

Wu, T. Yao-tsu and Whitney, A. K. (1973) Variational Calculus Involving Singular Integral Equations. ZAMM - Journal of Applied Mathematics, 53 (11). pp. 737-749. ISSN 0044-2267. doi:10.1002/zamm.19730531103.

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A new class of optimization problems arising in fluid mechanics can be characterized mathematically as equivalent to extremizing a functional in which the two unknown argument functions are related by a singular Cauchy integral equation. Analysis of the first variation of the functional yields a set of dual, nonlinear, integral equations, as opposed to the Euler differential equation in classical theory. A necessary condition for the extremum to be a minimum is derived from consideration of the second variation. Analytical solutions by singular integral equation methods and by the Rayleigh‐Ritz method are discussed for the linearized theory. The general features of these solutions are demonstrated by numerical examples.

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Additional Information:© 1973 WILEY‐VCH. Manuscript received: 9 January 1973. Funding Information: U. S. Navy. Grant Number: N 00014‐67‐A‐0094‐0011
Funding AgencyGrant Number
Office of Naval Research (ONR)N00014-67-A-0094-0011
Issue or Number:11
Record Number:CaltechAUTHORS:20200226-133730986
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Official Citation:Wu, T.Y.‐T. and Whitney, A.K. (1973), Variational Calculus Involving Singular Integral Equations. Z. angew. Math. Mech., 53: 737-749. doi:10.1002/zamm.19730531103
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:101581
Deposited By: George Porter
Deposited On:26 Feb 2020 22:30
Last Modified:16 Nov 2021 18:04

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