On the controllability of entropy solutions of scalar conservation laws at a junction via Lyapunov methods

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dc.contributor.authorDe Nitti, Nicola
dc.contributor.authorZuazua, Enrique
dc.date.accessioned2025-07-11T07:58:56Z
dc.date.available2025-07-11T07:58:56Z
dc.date.issued2023-01-04
dc.date.updated2025-07-11T07:58:56Z
dc.description.abstractIn this note, we prove a controllability result for entropy solutions of scalar conservation laws on a star-shaped graph. Using a Lyapunov-type approach, we show that, under a monotonicity assumption on the flux, if u and v are two entropy solutions corresponding to different initial data and same in-flux boundary data (at the exterior nodes of the star-shaped graph), then u ≡ v for a sufficiently large time. In order words, we can drive u to the target profile v in a sufficiently large control time by inputting the trace of v at the exterior nodes as in-flux boundary data for u. This result can also be shown to hold on tree-shaped networks by an inductive argument. We illustrate the result with some numerical simulations.en
dc.description.sponsorshipThis work has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement NO: 694126-DyCon), the Air Force Office of Scientific Research (AFOSR) under Award NO: FA9550-18-1-0242, the Grant MTM2017-92996-C2-1-R COSNET of MINECO (Spain), the Alexander von Humboldt-Professorship program, the European Unions Horizon 2020 research and innovation programme under the Marie SklodowskaCurie grant agreement No.765579-ConFlex, and the Transregio 154 Project “Mathematical Modelling Simulation and Optimization Using the Example of Gas Networks” of the Deutsche Forschungsgemeinschaft.en
dc.identifier.citationDe Nitti, N., & Zuazua, E. (2023). On the controllability of entropy solutions of scalar conservation laws at a junction via Lyapunov methods. Vietnam Journal of Mathematics, 51(1), 71-88. https://doi.org/10.1007/S10013-022-00598-9
dc.identifier.doi10.1007/S10013-022-00598-9
dc.identifier.eissn2305-2228
dc.identifier.issn2305-221X
dc.identifier.urihttps://hdl.handle.net/20.500.14454/3199
dc.language.isoeng
dc.publisherSpringer
dc.rights© The Author(s) 2023
dc.subject.otherControllability
dc.subject.otherEntropy solutions
dc.subject.otherLyapunov
dc.subject.otherNetworks
dc.subject.otherScalar conservation laws
dc.subject.otherStar-shaped graphs
dc.subject.otherTree-shaped graphs
dc.titleOn the controllability of entropy solutions of scalar conservation laws at a junction via Lyapunov methodsen
dc.typejournal article
dcterms.accessRightsopen access
oaire.citation.endPage88
oaire.citation.issue1
oaire.citation.startPage71
oaire.citation.titleVietnam Journal of Mathematics
oaire.citation.volume51
oaire.versionCVoR
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