ERVEDOZA, Sylvain; ZHANG, Jiacheng; WANG, Zhiqiang

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ERVEDOZA, Sylvain
Institut de Mathématiques de Bordeaux [IMB]

ZHANG, Jiacheng
School of Mathematical Sciences [Fudan]

WANG, Zhiqiang
School of Mathematical Sciences [Fudan]

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Article de revue

Ce document a été publié dans

Mathematical Control and Related Fields. 2023-05

AIMS

Résumé en anglais

In this article, we consider an inverse problem for the non-local system $\partial_{t} \rho +\lambda(W(t))\partial_x\rho=0$, in which $\displaystyle W(t)=\int_0^1 \rho(x,t)dx$ is the total mass of the system. We propose an algorithm and derive a formula to reconstruct the velocity function $\lambda(\cdot)$, assumed to be strictly positive, in an interval $[W_{-},W_+]$ which contains the initial total mass $W(0)$, by suitably choosing the influx condition $u(t) = \lambda(W(t)) \rho(0,t)$ and measuring the outflux $y(t) = \lambda(W(t)) \rho(1,t)$. Some numerical experiments are provided to illustrate the performance of our method.< Réduire

Mots clés en anglais

Transport equation

inverse problem

non-local velocity

URI

https://oskar-bordeaux.fr/handle/20.500.12278/190394

Project ANR

Nouvelles directions en contrôle et stabilisation: Contraintes et termes non-locaux - ANR-20-CE40-0009

Origine

Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251