dc.contributor.author | Bárcena Petisco, Jon Asier | |
dc.contributor.author | Fernández Cara, Enrique | |
dc.contributor.author | Souza, Diego A. | |
dc.date.accessioned | 2024-02-08T08:06:38Z | |
dc.date.available | 2024-02-08T08:06:38Z | |
dc.date.issued | 2023-12-15 | |
dc.identifier.citation | Journal of Differential Equations 376 : 126-153 (2023) | es_ES |
dc.identifier.issn | 0022-0396 | |
dc.identifier.uri | http://hdl.handle.net/10810/64888 | |
dc.description.abstract | This paper deals with the boundary exact controllability to the trajectories of the one-phase Stefan problem in one spatial dimension. This is a free-boundary problem that models solidification and melting processes. We prove the local exact controllability to (smooth) trajectories. To this purpose, we first reformulate the problem as the local null controllability of a coupled PDE-ODE system with distributed controls. Then, a new Carleman inequality for the adjoint of the linearized PDE-ODE system, coupled on the boundary through nonlocal in space and memory terms, is presented. This leads to the null controllability of an appropriate linear system. Finally, the result is obtained via local inversion, by using Liusternik-Graves’ Theorem. As a byproduct of our approach, we find that some parabolic equations which contains memory terms located on the boundary are null-controllable. | es_ES |
dc.description.sponsorship | EFC and DAS were partially supported by Grant PID2020–114976GB–I00, funded by MCIN/AEI/10.13039/501100011033. DAS was partially supported by Grant IJC2018–037863-I funded by MCIN/AEI/10.13039/501100011033. JABP was supported by the Grant PID2021-126813NB-I00 funded by MCIN/AEI/10.13039/501100011033 and by “ERDF A way of making Europe”, and by the grant IT1615-22 funded by the Basque Government. | es_ES |
dc.language.iso | eng | es_ES |
dc.publisher | Elsevier | es_ES |
dc.relation | info:eu-repo/grantAgreement/MICINN/PID2020–114976GB–I00 | |
dc.relation | info:eu-repo/grantAgreement/MICINN/PID2021-126813NB-I00 | |
dc.rights | info:eu-repo/semantics/embargoedAccess | es_ES |
dc.rights.uri | https://creativecommons.org/licenses/by-nc-nd/4.0/ | |
dc.subject | free-boundary problems | es_ES |
dc.subject | one-phase Stefan problem | es_ES |
dc.subject | exact controllability to the trajectories | es_ES |
dc.subject | Carleman inequalities | es_ES |
dc.subject | inverse function theorem | es_ES |
dc.title | Exact controllability to the trajectories of the one-phase Stefan problem | es_ES |
dc.type | info:eu-repo/semantics/article | es_ES |
dc.rights.holder | © 2023 Elsevier Inc. under CC BY-NC-ND licence (https://creativecommons.org/licenses/by-nc-nd/4.0/ | |
dc.relation.publisherversion | https://www.sciencedirect.com/science/article/pii/S0022039623005508 | |
dc.identifier.doi | 10.1016/j.jde.2023.08.016 | |
dc.departamentoes | Matemáticas | es_ES |
dc.departamentoeu | Matematika | es_ES |
dc.identifier.eissn | 1090-2732 | |