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Shape optimization in problems governed by generalised Navier-Stokes equations: existence analysis

Haslinger J., Malek J., Stebel J.

Control and Cybernetics

2005

Vol. 34, no 1

283-303

We study a shape optimization problem for a paper machine headbox which distributes a mixture of water and wood fibers in the paper manufacturing process. The aim is to find a shape which a priori ensures the given velocity profile on the outlet part. The mathematical formulation leads to an optimal control problem in which the control variable is the shape of the domain representing the header, the state problem is represented by the generalised Navier-Stokes system with nontrivial boundary conditions. The objective of this paper is to prove the existence of an optimal shape.