Local null controllability of the penalized Boussinesq system with a reduced number of controls
| hal.structure.identifier | Universidad Autónoma de Madrid [UAM] | |
| hal.structure.identifier | Fundación Deusto | |
| dc.contributor.author | BÁRCENA-PETISCO, Jon Asier | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| hal.structure.identifier | Control And GEometry [CaGE ] | |
| hal.structure.identifier | Laboratoire Jacques-Louis Lions [LJLL (UMR_7598)] | |
| dc.contributor.author | BALC'H, Kévin Le | |
| dc.date.accessioned | 2024-04-04T02:46:26Z | |
| dc.date.available | 2024-04-04T02:46:26Z | |
| dc.date.issued | 2022 | |
| dc.identifier.issn | 2156-8472 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/191551 | |
| dc.description.abstractEn | In this paper we consider the Boussinesq system with homogeneous Dirichlet boundary conditions and defined in a regular domain Ω ⊂ R^N for N = 2 and N = 3. The incompressibility condition of the fluid is replaced by its approximation by penalization with a small parameter ε > 0. We prove that our system is locally null controllable using a control with a restricted number of components, defined in an open set ω contained in Ω and whose cost is bounded uniformly when ε → 0. The proof is based on a linearization argument and the null-controllability of the linearized system is obtained by proving a new Carleman estimate for the adjoint system. This observability inequality is obtained thanks to the coercivity of some second order differential operator involving crossed derivatives. | |
| dc.description.sponsorship | Initiative d'excellence de l'Université de Bordeaux - ANR-10-IDEX-0003 | |
| dc.language.iso | en | |
| dc.publisher | AIMS | |
| dc.subject.en | Carleman inequality | |
| dc.subject.en | Controllability | |
| dc.subject.en | Nonlinear system | |
| dc.subject.en | Penalized Stokes system | |
| dc.title.en | Local null controllability of the penalized Boussinesq system with a reduced number of controls | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.3934/mcrf.2021038 | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| dc.description.sponsorshipEurope | Dynamic Control and Numerics of Partial Differential Equations | |
| bordeaux.journal | Mathematical Control and Related Fields | |
| bordeaux.page | 641 | |
| bordeaux.volume | 12 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 3 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-02913358 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-02913358v1 | |
| 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=2022&rft.volume=12&rft.issue=3&rft.spage=641&rft.epage=641&rft.eissn=2156-8472&rft.issn=2156-8472&rft.au=B%C3%81RCENA-PETISCO,%20Jon%20Asier&BALC'H,%20K%C3%A9vin%20Le&rft.genre=article |
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