Mostrar el registro sencillo del ítem
Null-controllability for weakly dissipative heat-like equations
| hal.structure.identifier | Unité de Mathématiques Pures et Appliquées [UMPA-ENSL] | |
| dc.contributor.author | ALPHONSE, Paul | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | KOENIG, Armand | |
| dc.date.accessioned | 2024-04-04T02:33:17Z | |
| dc.date.available | 2024-04-04T02:33:17Z | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/190461 | |
| dc.description.abstractEn | We study the null-controllability properties of heat-like equations posed on the whole Euclidean space $\mathbb R^n$. These evolution equations are associated with Fourier multipliers of the form $\rho(\vert D_x\vert)$, where $\rho\colon[0,+\infty)\rightarrow\mathbb C$ is a measurable function such that $\Re\rho$ is bounded from below. We consider the ``weakly dissipative'' case, a typical example of which is given by the fractional heat equations associated with the multipliers $\rho(\xi) = \xi^s$ in the regime $s\in(0,1)$, for which very few results exist. We identify sufficient conditions and necessary conditions on the control supports for the null-controllability to hold. More precisely, we prove that these equations are null-controllable in any positive time from control supports which are sufficiently thick at all scales. Under assumptions on the multiplier $\rho$, in particular assuming that $\rho(\xi) = o(\xi)$, we also prove that the null-controllability implies that the control support is thick at all scales, with an explicit lower bound of the thickness ratio in terms of the multiplier $\rho$.Finally, using Smith-Volterra-Cantor sets, we provide examples of non-trivial control supports that satisfy these necessary or sufficient conditions. | |
| dc.description.sponsorship | Centre International de Mathématiques et d'Informatique (de Toulouse) - ANR-11-LABX-0040 | |
| dc.language.iso | en | |
| dc.subject.en | Null-controllability | |
| dc.subject.en | Diffusive equations | |
| dc.subject.en | $\gamma$-thick sets | |
| dc.subject.en | Cantor-Smith-Volterra sets | |
| dc.title.en | Null-controllability for weakly dissipative heat-like equations | |
| dc.type | Document de travail - Pré-publication | |
| dc.type | Prepublication/Preprint | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| dc.identifier.arxiv | 2309.07533 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| hal.identifier | hal-03913881 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-03913881v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=ALPHONSE,%20Paul&KOENIG,%20Armand&rft.genre=preprint&unknown |
Archivos en el ítem
| Archivos | Tamaño | Formato | Ver |
|---|---|---|---|
|
No hay archivos asociados a este ítem. |
|||