On Unique Solutions of Multiple-State Optimal Design Problems on an Annulus

Krešimir Burazin ()
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Krešimir Burazin: University of Osijek

Journal of Optimization Theory and Applications, 2018, vol. 177, issue 2, No 4, 329-344

Abstract: Abstract We study the uniqueness and explicit derivation of the relaxed optimal solutions, corresponding to the minimization of weighted sum of potential energies for a mixture of two isotropic conductive materials on an annulus. Recently, it has been shown by Burazin and Vrdoljak that even for multiple-state problems, if the domain is spherically symmetric, then the proper relaxation of the problem by the homogenization method is equivalent to a simpler relaxed problem, stated only in terms of local proportions of given materials. This enabled explicit calculation of a solution on a ball, while problems on an annulus appeared to be more tedious. In this paper, we discuss the uniqueness of a solution of this simpler relaxed problem, when the domain is an annulus and we use the necessary and sufficient conditions of optimality to present a method for explicit calculation of the unique solution of this simpler proper relaxation, which is demonstrated on an example.

Keywords: Stationary diffusion; Optimal design; Homogenization; Optimality conditions; 80A20; 49J20; 80M40; 49K35 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10957-018-1284-7

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