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Shape optimization in problems governed by generalised Navier-Stokes equations: existence analysis. (English) Zbl 1167.49328
Summary: 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.

49Q10 Optimization of shapes other than minimal surfaces
35Q35 PDEs in connection with fluid mechanics
49N90 Applications of optimal control and differential games
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
76A05 Non-Newtonian fluids
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