Uniform Turnpike property and singular limits

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dc.contributor.authorHernández Salinas, Martín Sebastián
dc.contributor.authorZuazua, Enrique
dc.date.accessioned2025-04-15T14:07:36Z
dc.date.available2025-04-15T14:07:36Z
dc.date.issued2024-04
dc.date.updated2025-04-15T14:07:36Z
dc.description.abstractMotivated by singular limits for long-time optimal control problems, we investigate a class of parameter-dependent parabolic equations. First, we prove a turnpike result, uniform with respect to the parameters within a suitable regularity class and under appropriate bounds. The main ingredient of our proof is the justification of the uniform exponential stabilization of the corresponding Riccati equations, which is derived from the uniform null control properties of the model. Then, we focus on a heat equation with rapidly oscillating coefficients. In the one-dimensional setting, we obtain a uniform turnpike property with respect to the highly oscillatory heterogeneous medium. Afterward, we establish the homogenization of the turnpike property. Finally, our results are validated by numerical experimentsen
dc.description.sponsorshipM. Hernandez has been funded by the Transregio 154 Project, “Mathematical Modelling,Simulation, and Optimization Using the Example of Gas Networks” of the DFG, project C07, and the fellowship “ANID-DAAD bilateral agreement” 57600326. E. Zuazua has been funded by the Alexander von Humboldt-Professorship program, the ModConFlex Marie Curie Action, HORIZON-MSCA-2021-DN-01, the COST Action MAT-DYN-NET, the Transregio 154 Project “Mathematical Modelling, Simulation and Optimization Using the Example of Gas Networks” of the DFG, grants PID2020-112617GB-C22 and TED2021-131390B-I00 of MINECO (Spain). Madrid Government- UAM Agreement for the Excellence of the University Research Staff in the context of the V PRICIT (Regional Programme of Research and Technological Innovation)en
dc.identifier.citationHernández, M., & Zuazua, E. (2024). Uniform Turnpike property and singular limits. Acta Applicandae Mathematicae, 190(1). https://doi.org/10.1007/S10440-024-00640-7
dc.identifier.doi10.1007/S10440-024-00640-7
dc.identifier.eissn1572-9036
dc.identifier.issn0167-8019
dc.identifier.urihttp://hdl.handle.net/20.500.14454/2625
dc.language.isoeng
dc.publisherSpringer Science and Business Media B.V.
dc.rights© The Author(s) 2024
dc.subject.otherLong time behavior
dc.subject.otherOptimal control problems
dc.subject.otherRapidly oscillating linear parabolic equation
dc.subject.otherSingular limits problems
dc.subject.otherTurnpike property
dc.subject.otherUniform controllability
dc.titleUniform Turnpike property and singular limitsen
dc.typejournal article
dcterms.accessRightsopen access
oaire.citation.issue1
oaire.citation.titleActa Applicandae Mathematicae
oaire.citation.volume190
oaire.licenseConditionhttps://creativecommons.org/licenses/by/4.0/
oaire.versionVoR
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