Inverse Design and Boundary Controllability for the Chromatography System

Abstract

AbstractWe consider the prototypical example of the $$2\times 2$$ 2 × 2 liquid chromatography system and characterize the set of initial data leading to a given attainable profile at $$t=T$$ 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 $$L^2$$ 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.