INVERSE DESIGN AND BOUNDARY CONTROLLABILITY FOR THE CHROMATOGRAPHY SYSTEM
Résumé
We consider the prototypical example of the 2 × 2 liquid chromatography system and characterize the set of initial data leading to a given attainable profile at t = T. For profiles that are not attainable at time T , we study a non-smooth optimization problem: recovering the initial data that lead as close as possible to the target in the L 2-norm. We then study the system on a bounded domain and use a boundary control to steer its dynamics to a given trajectory. Finally, we implement a suitable finite volumes scheme to illustrate these results and show its numerical convergence. Minor modifications of our arguments apply to the Keyfitz-Kranzer system.
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