ED Mathématiques et Informatique
Some applications of harmonic analysis to control theory
by Yunlei WANG (IMB - Institut de Mathématiques de Bordeaux)
The defense will take place at 15h00 - Salle 2 de l'IMB Institut de Mathématiques de Bordeaux UMR 5251 Université de Bordeaux 351, Cours de la Libération F-33405 TALENCE
in front of the jury composed of
- Philippe JAMING - Professeur des universités - Université de Bordeaux - Directeur de these
- Jérôme LE ROUSSEAU - Professeur - Université Sorbonne Paris Nord - Rapporteur
- Karine BEAUCHARD - Professeure - École normale supérieure de Rennes - Examinateur
- Marius TUCSNAK - Professeur - Université de Bordeaux - Examinateur
- Emmanuel TRELAT - Professeur - Sorbonne Université - Rapporteur
- Jiuyi ZHU - Associate Professor - Louisiana State University - Examinateur
This thesis investigates fundamental questions in the control theory and observability analysis of partial differential equations, focusing on two interconnected themes: null-controllability of parabolic systems via spectral inequalities, and observability of dispersive equations through harmonic analytic methods. The first theme centers on spectral inequalities and their role in the null-controllability of heat-like equations. For one-dimensional Schrödinger operators, we derive new spectral inequalities on thick sets with decaying density by leveraging propagation of smallness properties for solutions of elliptic equations in the plane. These inequalities enable us to deduce null-controllability results directly via the Lebeau-Robbiano method. Additionally, we analyze Baouendi–Grushin operators by constructing spectral inequalities with explicit dependence on potential parameters. This leads to null-controllability for Baouendi–Grushin heat-like equations posed on equidistributed vertical strips, expanding prior results on hypoelliptic operators. The second theme investigates $L^2$- and $L^1$-norm estimates for nonharmonic trigonometric polynomials with sparse frequencies and their applications to observability in dispersive equations. For linear dispersive equations on the torus, we link Ingham's inequality to observability criteria for line segments defined by their slopes. We also establish lower bounds for $L^1$-norms of nonharmonic trigonometric polynomials. This can be applied to establish $L^1$-observability estimates for PDEs such as the free Schrödinger equation.
ED Droit
Glass, building, material and the law
by Jean-Marie GOIZET (INSTITUT DE RECHERCHE EN DROIT DES AFFAIRES ET DU PATRIMOINE)
The defense will take place at 14h15 - salle de thèse Université de Montaigne Montesquieu 19 esplanade des Antilles 33607 PESSAC
in front of the jury composed of
- Jean-Marie PLAZY - Professeur agrégé - Université de Bordeaux - Directeur de these
- Aline VIGNON-BARRAULT - Professeur agrégé - Université d'ANGERS - Rapporteur
- Annie CHAMOULAUD-TRAPIERS - Professeure agrégée - Université de Limoges - Rapporteur
- Philippe DELMAS SAINT HILAIRE - Professeur agrégé - Université de Bordeaux - Examinateur
Glass has become an essential building material for the construction of buildings. Its qualities are simultaneously its flaws (transparency, translucency, fragility), which make it a unique material different from others, subjecting it to its own legal challenges. It is transparent, allowing visibility from the inside to the outside and vice versa. However, everyone wants to maintain their privacy. People wish to see without being seen in their own homes, whether they are owners or not. Glass is therefore subject to the scrutiny of property rights. Although this right is no longer absolute, it remains an essential element of the quality of life for everyone. Thanks to glass, individuals can assert their right to sunlight, a right to views towards the horizon, and a right to the landscape—rights that are not legally recognized but may be upheld by the courts. The environment, therefore, is affected not only in its immediate context, including neighboring areas, but also in a much broader sense, concerning the protection of nature and the shared heritage of the Nation. Thus, environmental law limits the freedom of property owners. The environment is legally protected, and ecological harm due to pollution is punishable. Urban planning and construction laws also restrict this freedom. The purposes of these laws serve the public interest. Construction rules apply to all materials, especially glass, and have repercussions on neighborly relations. These relations influence urban planning documents. Furthermore, neighboring properties entail constraints stemming from easements that support the right to tranquility. The proximity of homes with their openings closed by glass materials is a source of conflicts that has necessitated regulations concerning views, light, and the joint ownership of walls. This dates back to the Civil Code and can only be seen as anachronistic. Current construction methods involve raising load-bearing pillars with gaps between them closed by non-load-bearing "curtain walls," which may be built entirely or in part from lighter materials such as glass. The rules of joint ownership do not apply to them; they can only concern load-bearing walls. The same applies to the windows, which are meticulously regulated by the Civil Code, making such regulations unnecessary with the introduction of translucent fixed glass blocks that prevent any ventilation, despite being suggested by some, at the risk of conflicts with neighbors (noise, odors). The evolution of the law is therefore necessary. Proposals exist, such as those from the Henri CAPITANT Association, which are open to improvement. Additionally, neighboring properties can lead to abuses of enjoyment that serve the rights of neighbors, such as the abuse of rights or abnormal disturbances from neighboring properties. Finally, glass is subject to the scrutiny of construction law. It gives rise to standards (construction contracts, technical rules, noise protection, safety of individuals, thermal insulation of buildings). It also generates liability that falls on all builders (project owners, architects, and all participants in the construction cycle). Glass, as a fragile material, is indeed a source of contractual liability (in the case of a hotelier) or delictual liability concerning inanimate things. Despite all the constraints and challenges, glass, as a legal object, will always remain an indispensable building material for future generations of builders, enabling them to continue benefiting from their environment.
ED Sciences Physiques et de l'Ingénieur
Air-filled Substrate Integrated Waveguide (AFSIW) emerging technology filtering subsystems for New-Space payloads
by Maxime LE GALL (Laboratoire de l'Intégration du Matériau au Système)
The defense will take place at 13h45 - Amphi Jean-Paul Dom 351 Cours de la Libération, 33405 Talence
in front of the jury composed of
- Anthony GHIOTTO - Maître de conférences - Université de Bordeaux - Directeur de these
- Pierre BLONDY - Professeur des universités - Université de Limoges - Rapporteur
- Raafat MANSOUR - Full professor - Université de Waterloo - Rapporteur
- Issam MARAH - Docteur - Exens Solutions - Examinateur
- Nhu Huan NGUYEN - Maître de conférences - Université de Grenoble Alpes - Examinateur
- Thierry TARIS - Professeur des universités - Université de Bordeaux - Examinateur
New Space has been reinventing the traditional space industry for the past two decades. This renewal is driven by developing innovative, low-cost, highly integrated, high-performance microwave technologies. Among these, the air-filled substrate-integrated waveguide (AFSIW), introduced in 2014, combines the low insertion losses of conventional waveguides with the integration and reduced costs of planar technologies. Previous research has shown that this technology effectively meets New Space requirements, particularly in the design of passive devices such as filters, couplers, and isolators. The goal is to explore this technology further, progressing from the circuit level, with the realization of innovative passive functions tested in space environments, to the system level, with the co-integration of both active and passive components.