Zeitschrift für Analysis und ihre Anwendungen
Vol. 18, No. 1, pp. 143-155 (1999)
Global Solution of Optimal Shape Design Problems
A. Fakharzadeh J. and J. E. RubioA. Fakharzadeh J.: Shahid Chamran University of Ahwaz, Dept. Math., Ahwaz, Iran; e-mail: email@example.com
J. E. Rubio: University of Leeds, Dept. Appl. Math. Studies, Leeds, LS2 9JT, UK
Abstract: We consider optimal shape design problems defined by pairs of geometrical elements and control functions associated with linear or nonlinear elliptic equations. First, necessary conditions are illustrated in a variational form. Then by applying an embedding process, the problem is extended into a measure-theoretical one, which has some advantages. The theory suggests the development of a computational method consisting of the solution of a finite-dimensional linear programming problem. Nearly optimal shapes and related controls can thus be constructed. Two examples are also given.
Keywords: embedding methods, optimal shape design, Radon measures, linear programming, optimal shape, optimal control, elliptic equations
Classification (MSC2000): 49-XX
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Electronic fulltext finalized on: 25 Apr 2000. This page was last modified: 9 Nov 2001.