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Paper   IPM / M / 11242
School of Mathematics
  Title:   Best domain for an elliptic problem in Cartesian coordinates by means of shape-measure
  Author(s):  A. Fakharzadeh Jahromi (Joint with J. E. Rubio)
  Status:   Published
  Journal: Asian Journal of Control
  Vol.:  11
  Year:  2009
  Pages:   536-547
  Supported by:  IPM
In (ZAA J. Anal. Appl., Vol. 16, No. 1, pp. 143-155) we introduced a method to determine the optimal domains for elliptic optimal-shape design problems in polar coordinates. However, the same problem in cartesian coor�dinates, which are more applicable, is found to be much harder, therefore we had to develop a new approach for these designs. Herein, the unknown domain is divided into a fixed and a variable part and the optimal pair of the domain and its optimal control, is characterized in two stages. Firstly, the optimal con�trol for the each given domain is determined by changing the problem into a measure-theoretical one, replacing this with an infinite dimensional linear programming problem and approximating schemes; then the nearly optimal control function is characterized. Therefore a function that offers the optimal value of the objective function for a given domain, is defined. In the second stage, by applying a standard optimization method, the global minimizer pair will be obtained. Some numerical examples are also given.

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