Null-controllability properties of a fractional wave equation with a memory term
| dc.contributor.author | Biccari, Umberto | |
| dc.contributor.author | Warma, Mahamadi | |
| dc.date.accessioned | 2025-01-23T14:15:47Z | |
| dc.date.available | 2025-01-23T14:15:47Z | |
| dc.date.issued | 2020-06 | |
| dc.date.updated | 2025-01-23T14:15:47Z | |
| dc.description.abstract | We study the null-controllability properties of a one-dimensional wave equation with memory associated with the fractional Laplace operator. The goal is not only to drive the displacement and the velocity to rest at some time-instant but also to require the memory term to vanish at the same time, ensuring that the whole process reaches the equilibrium. The problem being equivalent to a coupled nonlocal PDE-ODE system, in which the ODE component has zero velocity of propagation, we are required to use a moving control strategy. Assuming that the control is acting on an open subset ω(t) which is moving with a constant velocity c ∈ R, the main result of the paper states that the equation is null controllable in a sufficiently large time T and for initial data belonging to suitable fractional order Sobolev spaces. The proof will use a careful analysis of the spectrum of the operator associated with the system and an application of a classical moment method. | en |
| dc.description.sponsorship | The work of the first author is supported by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement NO: 694126-DyCon), by the Grant MTM2017-92996-C2-1-R COSNET of MINECO (Spain), and by the ELKARTEK project KK-2018/00083 ROAD2DC of the Basque Government. The work of both authors is supported by the Air Force Office of Scientific Research (AFOSR) under Award NO: FA9550-18-1-0242 | en |
| dc.identifier.citation | Biccari, U., & Warma, M. (2020). Null-controllability properties of a fractional wave equation with a memory term. Evolution Equations and Control Theory, 9(2), 399-430. https://doi.org/10.3934/EECT.2020011 | |
| dc.identifier.doi | 10.3934/EECT.2020011 | |
| dc.identifier.eissn | 2163-2480 | |
| dc.identifier.issn | 2163-2472 | |
| dc.identifier.uri | http://hdl.handle.net/20.500.14454/2241 | |
| dc.language.iso | eng | |
| dc.publisher | American Institute of Mathematical Sciences | |
| dc.subject.other | Fractional wave equation | |
| dc.subject.other | Memory | |
| dc.subject.other | Moment method | |
| dc.subject.other | Moving control | |
| dc.subject.other | Null controllability | |
| dc.title | Null-controllability properties of a fractional wave equation with a memory term | en |
| dc.type | journal article | |
| dcterms.accessRights | metadata only access | |
| oaire.citation.endPage | 430 | |
| oaire.citation.issue | 2 | |
| oaire.citation.startPage | 399 | |
| oaire.citation.title | Evolution Equations and Control Theory | |
| oaire.citation.volume | 9 |