engleski

Multiple state optimal design problems with random perturbation

A multiple state optimal design problem with presence of uncertainty on the right-hand side is considered, in context of stationary diffusion with two isotropic phases. Perturbation term is given by a random function on a probability space. Similar problem with one state equation is considered in \cite{; ; BM}; ; . We shall address the question of relaxation by the homogenization method and necessary conditions of optimality. The case of discrete probability space leads to another multiple state problem (possibly with infinite number of states), which could be treated by similar techniques to those presented in \cite{; ; A, V}; ; . Relaxation can be expressed in a simpler form for problems with spherical symmetry in case of minimization (or maximization) of convex combination of compliances.

optimal design ; multiple state ; random perturbation

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