色谱系统的逆向设计和边界可控性

IF 1.2 3区数学 Q1 MATHEMATICS

Milan Journal of Mathematics Pub Date : 2024-09-04 DOI:10.1007/s00032-024-00402-y

Giuseppe Maria Coclite, Nicola De Nitti, Carlotta Donadello, Florian Peru

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引用次数: 0

摘要

我们考虑了液相色谱系统的原型，并描述了在 \(t=T\) 时导致给定可实现剖面的初始数据集的特征。对于在 T 时无法实现的剖面，我们研究了一个非平滑优化问题：恢复初始数据，使其尽可能接近 \(L^2\)-norm 中的目标。然后，我们在有界域上研究该系统，并使用边界控制将其动态转向给定轨迹。最后，我们采用合适的有限体积方案来说明这些结果，并展示其数值收敛性。我们对Keyfitz-Kranzer系统的论证稍作修改即可应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Inverse Design and Boundary Controllability for the Chromatography System

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Inverse Design and Boundary Controllability for the Chromatography System

We consider the prototypical example of the \(2\times 2\) 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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来源期刊

Milan Journal of Mathematics 数学-数学

CiteScore

2.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Milan Journal of Mathematics (MJM) publishes high quality articles from all areas of Mathematics and the Mathematical Sciences. The authors are invited to submit "articles with background", presenting a problem of current research with its history and its developments, the current state and possible future directions. The presentation should render the article of interest to a wider audience than just specialists. Many of the articles will be "invited contributions" from speakers in the "Seminario Matematico e Fisico di Milano". However, also other authors are welcome to submit articles which are in line with the "Aims and Scope" of the journal.