Applications of Mathematics, Vol. 64, No. 2, pp. 195-224, 2019

Shape optimization for a time-dependent model of a carousel press in glass production

Petr Salač, Jan Stebel

Received October 30, 2018.   Published online March 18, 2019.

Abstract:  This contribution presents the shape optimization problem of the plunger cooling cavity for the time dependent model of pressing the glass products. The system of the mould, the glass piece, the plunger and the plunger cavity is considered in four consecutive time intervals during which the plunger moves between 6 glass moulds. The state problem is represented by the steady-state Navier-Stokes equations in the cavity and the doubly periodic energy equation in the whole system, under the assumption of rotational symmetry, supplemented by suitable boundary conditions. The cost functional is defined as the squared weighted $ L^2 $ norm of the difference between a prescribed constant and the temperature of the plunger surface layer at the moment before separation of the plunger and the glass piece. The existence and uniqueness of the solution to the state problem and the existence of a solution to the optimization problem are proved.
Keywords:  shape optimization; Navier-Stokes equations; heat transfer
Classification MSC:  49Q10, 76D55, 93C20
DOI:  10.21136/AM.2019.0301-18

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Affiliations:   Petr Salač, Jan Stebel, Technical University of Liberec, Studentská 2, 461 17 Liberec 1, Czech Republic, e-mail:,

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