Recovering the velocity in a 1-d non-local transport equation
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | ERVEDOZA, Sylvain | |
| hal.structure.identifier | School of Mathematical Sciences [Fudan] | |
| dc.contributor.author | ZHANG, Jiacheng | |
| hal.structure.identifier | School of Mathematical Sciences [Fudan] | |
| dc.contributor.author | WANG, Zhiqiang | |
| dc.date.accessioned | 2024-04-04T02:32:32Z | |
| dc.date.available | 2024-04-04T02:32:32Z | |
| dc.date.issued | 2023-05 | |
| dc.identifier.issn | 2156-8472 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/190394 | |
| dc.description.abstractEn | 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. | |
| dc.description.sponsorship | Nouvelles directions en contrôle et stabilisation: Contraintes et termes non-locaux - ANR-20-CE40-0009 | |
| dc.language.iso | en | |
| dc.publisher | AIMS | |
| dc.subject.en | Transport equation | |
| dc.subject.en | inverse problem | |
| dc.subject.en | non-local velocity | |
| dc.title.en | Recovering the velocity in a 1-d non-local transport equation | |
| dc.type | Article de revue | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| bordeaux.journal | Mathematical Control and Related Fields | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-04288054 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-04288054v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Mathematical%20Control%20and%20Related%20Fields&rft.date=2023-05&rft.eissn=2156-8472&rft.issn=2156-8472&rft.au=ERVEDOZA,%20Sylvain&ZHANG,%20Jiacheng&WANG,%20Zhiqiang&rft.genre=article |
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