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Topological Optimization and Optimal Transport by Filippo Santambrogio, Thierry Champion, Guillaume Carlier, Martin Rumpf, Édouard Oudet, Maïtine Bergounioux

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M. Hintermüller and D. Wegner

3 Distributed and boundary control problems for the semidiscrete Cahn–Hilliard/Navier–Stokes system with nonsmooth Ginzburg–Landau energies

M. Hintermüller, Humboldt-Universität zu Berlin, Department of Mathematics, Germany

D. Wegner, Humboldt-Universität zu Berlin, Department of Mathematics, Germany

Abstract: This chapter is concerned with optimal control problems for the coupled Cahn–Hilliard (CH)/Navier–Stokes (NS) system related to ‘model H’ of Hohenberg and Halperin [20]. It proposes a time discretization allowing suitable energy estimates, that in particular force the total energy to decrease without control action, and it considers distributed as well as boundary control of the fluid. For nonsmooth potentials, ...

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