Naslov
Exact Solutions in Optimal Design Problems for Stationary Diffusion Equation

Autori
Burazin, Krešimir ; Vrdoljak, Marko

Izvornik
Acta applicandae mathematicae (0167-8019) 161 (2019), 1; 71-88

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Stationary diffusion ; Optimal design ; Homogenization ; Saddle point ; Optimality conditions

Sažetak
We consider two-phase multiple state optimal design problems for stationary diffusion equation. Both phases are taken to be isotropic, and the goal is to find the optimal distribution of materials within domain, with prescribed amounts, that minimizes a weighted sum of energies. In the case of one state equation, it is known that the proper relaxation of the problem via the homogenization theory is equivalent to a simpler relaxed problem, stated only in terms of the local proportion of given materials. We prove an analogous result for multiple state problems if the number of states is less than the space dimension. In spherically symmetric case, the result holds for arbitrary number of states, and the optimality conditions of a simpler relaxation problem, which are necessary and sufficient, enable us to explicitly calculate the unique solution of proper relaxation for some examples. In contrary to maximization problems, these solutions are not classical.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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