Necessary conditions for optimal design in hyperbolic problems (CROSBI ID 537683)
Prilog sa skupa u zborniku | sažetak izlaganja sa skupa | međunarodna recenzija
Podaci o odgovornosti
Vrdoljak, Marko
engleski
Necessary conditions for optimal design in hyperbolic problems
We consider optimal design with hyperbolic initial boundary value problem as the state equation. As a possible application consider a body obtained by mixing different materials which is vibrating under the given external force and prescribed boundary and initial values. The control function (distribution of given materials in a given domain) uniquely determines the response (state function) of the vibrating material. Our goal is to find distribution of materials minimising given integral functional (cost) depending on state and control functions. As it is common in optimal design problems, the relaxation is needed, introducing the notion of composite materials as fine mixtures of different phases, mathematically described by the homogenisation theory. This approach enables us to calculate the G\^ateaux derivative of the cost functional, leading to the necessary conditions of optimality. This method proved very successful in optimal design in elliptic problems, since it yields interesting theoretical results as well as important numerical algorithms.
optimal design; hyperbolic equation; homogenisation
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Podaci o prilogu
39-39.
2007.
objavljeno
Podaci o matičnoj publikaciji
Applied mathematics and scientific computing
Tambača, Josip et al.
Zagreb:
Podaci o skupu
Fifth Conference on Applied Mathematics and Scientific Computing
predavanje
09.07.2007-13.07.2007
Brijuni, Hrvatska