Averaged dynamics and control for heat equations with random diffusion

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dc.contributor.authorBárcena Petisco, Jon Asier
dc.contributor.authorZuazua, Enrique
dc.date.accessioned2025-06-06T10:15:30Z
dc.date.available2025-06-06T10:15:30Z
dc.date.issued2021-10-30
dc.date.updated2025-06-06T10:15:30Z
dc.description.abstractThis paper deals with the averaged dynamics for heat equations in the degenerate case where the diffusivity coefficient, assumed to be constant, is allowed to take the null value. First we prove that the averaged dynamics is analytic. This allows to show that, most often, the averaged dynamics enjoys the property of unique continuation and is approximately controllable. We then determine if the averaged dynamics is actually null controllable or not depending on how the density of averaging behaves when the diffusivity vanishes. In the critical density threshold the dynamics of the average is similar to the [Formula presented]-fractional Laplacian, which is well-known to be critical in the context of the controllability of fractional diffusion processes. Null controllability then fails (resp. holds) when the density weights more (resp. less) in the null diffusivity regime than in this critical regime.en
dc.description.sponsorshipThis project has also 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 work of the first author was also supported by grants from Région Ile-de-France. The work of the second author is also partially supported by the Air Force Office of Scientific Research (AFOSR), United States under Award NO: FA9550-18-1-0242, by the Grant MTM2017-92996-C2-1-R COSNET of MINECO (Spain), by the Alexander von Humboldt-Professorship program, the European Unions Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No.765579- ConFlex, and the Transregio 154 Project ‘‘Mathematical Modelling, Simulation and Optimization Using the Example of Gas Networks’’ of the German DFG, Germanyen
dc.identifier.citationBárcena-Petisco, J. A., & Zuazua, E. (2021). Averaged dynamics and control for heat equations with random diffusion. Systems and Control Letters, 158. https://doi.org/10.1016/J.SYSCONLE.2021.105055
dc.identifier.doi10.1016/J.SYSCONLE.2021.105055
dc.identifier.issn0167-6911
dc.identifier.urihttps://hdl.handle.net/20.500.14454/2957
dc.language.isoeng
dc.publisherElsevier B.V.
dc.rights© 2021 The Author(s)
dc.subject.otherAveraged controllability
dc.subject.otherAveraged observability
dc.subject.otherObservability
dc.subject.otherRandom heat equation
dc.titleAveraged dynamics and control for heat equations with random diffusionen
dc.typejournal article
dcterms.accessRightsopen access
oaire.citation.titleSystems and Control Letters
oaire.citation.volume158
oaire.licenseConditionhttps://creativecommons.org/licenses/by/4.0/
oaire.versionVoR
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