Null controllability of linear and semilinear nonlocal heat equations with an additive integral kernel
| dc.contributor.author | Biccari, Umberto | |
| dc.contributor.author | Hernández Santamaría, Víctor | |
| dc.date.accessioned | 2024-12-12T10:40:30Z | |
| dc.date.available | 2024-12-12T10:40:30Z | |
| dc.date.issued | 2019 | |
| dc.date.updated | 2024-12-12T10:40:30Z | |
| dc.description.abstract | We consider a linear nonlocal heat equation in a bounded domain Ω ⊂ ℝ with Dirichlet boundary conditions. The nonlocality is given by the presence of an integral kernel. We analyze the problem of controllability when the control acts on an open subset of the domain. It is by now known that the system is null controllable when the kernel is time-independent and analytic or, in the one-dimensional case, in separated variables. In this paper, we relax this assumption and we extend the result to a more general class of kernels. Moreover, we get explicit estimates on the cost of null controllability that allow us to extend the result to some semilinear models. | en |
| dc.description.sponsorship | This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant agreement 694126-DyCon). The work of the first author was partially supported by grant MTM2017-92996-C2-1-R COSNET of MINECO (Spain), by ELKARTEK project KK-2018/00083 ROAD2DC of the Basque government, and by the Air Force Office of Scientific Research under award FA9550-18-1-0242 | en |
| dc.identifier.citation | Biccari, U., & Hernández-Santamaría, V. (2019). Null controllability of linear and semilinear nonlocal heat equations with an additive integral kernel. SIAM Journal on Control and Optimization, 57(4), 2924-2938. https://doi.org/10.1137/18M1218431 | |
| dc.identifier.doi | 10.1137/18M1218431 | |
| dc.identifier.issn | 0363-0129 | |
| dc.identifier.uri | http://hdl.handle.net/20.500.14454/2163 | |
| dc.language.iso | eng | |
| dc.publisher | Society for Industrial and Applied Mathematics Publications | |
| dc.rights | © 2019 Society for Industrial and Applied Mathematics | |
| dc.subject.other | Carleman inequalities | |
| dc.subject.other | Heat equation | |
| dc.subject.other | Linear | |
| dc.subject.other | Nonlocal terms | |
| dc.subject.other | Null controllability | |
| dc.subject.other | Semilinear systems | |
| dc.title | Null controllability of linear and semilinear nonlocal heat equations with an additive integral kernel | en |
| dc.type | journal article | |
| dcterms.accessRights | metadata only access | |
| oaire.citation.endPage | 2938 | |
| oaire.citation.issue | 4 | |
| oaire.citation.startPage | 2924 | |
| oaire.citation.title | SIAM Journal on Control and Optimization | |
| oaire.citation.volume | 57 |