Cette thèse est consacrée à l’étude de problèmes inverses associés à des équations aux dérivées partielles hyperboliques et de type Schrödinger.La première partie de la thèse est consacrée à l’étude de problèmes inverses pour l’équation des ondes. Il s’agit d’examiner les propriétés de stabilité et d’unicité dans l’identification de certains coefficients apparaissant dans l’équation des ondes, à partir de différents types d’observation.La deuxième partie de cette thèse, traite du problème de l’identification du champ magnétique et du potentiel électrique apparaissant dans l’équation du Schrödinger. Nous prouvons que ces coefficients peuvent être déterminés de façon stable dans tout le domaine, à partir de données de type Neumann. La dérivation de ces résultats est basée sur la construction d’un ensemble de solutions de type optique géométrique, adaptées au système étudié. Il existe une méthode alternative pour l’analyse de ce type de problèmes inverses, celle de Bukhgeim-Klibanov, qui utilise une estimation de Carleman spécifique à l’opérateur con-sidéré. Elle nous a permis de montrer qu’il est possible de récupérer de façon stable et simultanée, la partie spatiale des potentiels électrique et magnétique de l’équation de Schrödinger magnétique, à partir d’un nombre fini de mesures partielles de la solution. / This thesis is devoted to the study of inverse problems associated to hyperbolic and Schrödinger equations. The first part of the thesis is devoted to the study of inverse problemsfor the wave equation. The aim is to examine the stability andthe uniqueness issues in the identification of certain coefficients appearing in the wave equation from different types of observation. The second part of this thesis deals with the problem of the identification of a magnetic field and an electric potential appearing in the Schrödinger equation. We prove that these coefficients can be stably determined throughout the domain, using Neumann data. The derivation of these results is based on the construction of a set of geometric optics solutions adapted to the system studied. There is an alternative method for the analysis of this type of inverse problem, which is due to Bukhgeim-Klibanov, and which uses a Carleman estimate. We show that it is possible to stably and simultaneously recover the spatial part of the electrical and magnetic potentialsappearing in the magnetic Schrödinger equation, from a finite number of measurements.

Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico / Neste trabalho, foram estudadas as caracterÃsticas estruturais de nanopartÃculas de Ãxidos semicondutores SnO2 dopadas com ferro, atravÃs de difraÃÃo de raios-x e espectroscopia MÃssbauer. O composto em estudo (Sn1−xFexOy) foi preparado por moagem mecÃnica de altas energias e sol-gel proteico. As amostras preparadas por moagem apresentaram aumento de dopagem na matriz semicondutora como funÃÃo do tempo de moagem, mas tambÃm apresentaram impurezas indesejÃveis provenientes do recipiente e das esferas que foram utilizadas na sÃntese. Uma sÃrie de amostras com concentraÃÃes variadas de ferro foram lavadas com HCl e reanalisadas. Resultados obtidos dessas medidas mostram que o ferro entra na rede do SnO2 substituindo o Sn de forma aleatÃria independente da concentraÃÃo de ferro. TambÃm foi observado a formaÃÃo de um sÃtio de ferro com deficiÃncia de oxigÃnio que à atribuÃdo ao desbalanÃo estequiomÃtrico dos compostos precursores usados na moagem. Amostras de SnO2 nanoparticuladas foram sintetizados pelo mÃtodo sol-gel proteico com trÃs temperaturas de calcinaÃÃo. Foi observado que o tamanho de partÃcula à diretamente proporcional à temperatura de calcinaÃÃo. TambÃm por sol-gel proteico foram preparadas amostras de Sn0,90Fe0,10O2 nanoparticulado. Foi identificado que a temperatura de calcinaÃÃo de 400ÂC hà formaÃÃo de Fe2O3 espÃrio. Jà a 300ÂC a Ãnica fase presente à a de SnO2 dopada com ferro. Assim como nas amostras produzidas por moagem, essa amostra apresentou dois sÃtios de ferro como valores de quadrupolo menor do que na moagem indicando menor distorÃÃo da rede cristalina. A quantidade relativa de sÃtios com deficiÃncia de oxigÃnio à bem menor nas amostras preparadas por sol-gel mostrando que o composto produzido por sol-gel proteico possui uma concentraÃÃo mais estequiomÃtrica do que os preparados por moagem. / In this work structural characterization by x-ray diffraction and MÂossbauer spectroscopy of Fe-doped semiconducting oxide SnO2 nanoparticles is reported. The compound under study (Sn1−xFexOy) was prepared by high energy ball milling and proteic sol-gel. The samples prepared by ball milling showed an increase of Fe-doping in the semiconducting matrix as a function of milling time, as well as amounts of undesirable metallic iron impurities from the milling tools. A series of samples with various Fe concentrations were HCl-washed in order to eliminate the impurities. Results obtained from measurements on these samples showed that Fe enters the host matrix randomly replacing Sn in octahedral sites regardless of iron concentration. It was also showed the presence of oxygen deficient iron sites attributed to the stoichiometric unbalance of precursor materials used in the milling process. Samples of nanosized SnO2 were prepared by proteic sol-gel with three calcination temperatures. It was found that average particle sizes are directly proportional to the temperature. Nanostructured Sn90Fe10O2 was also synthesized by proteic sol-gel. Formation of spurious Fe2O3 was found at calcination temperature of 400ÂC. At 300ÂC, on the other hand, monophased Fe-doped SnO2 was achieved. Likewise the milled samples, this sample presented two different octahedral iron sites, although with quadrupole splitting slightly smaller than those for the milled samples indicating a less distorted crystal structure. The significantly smaller relative number of oxygen-deficient sites in the proteic sol-gel sample shows that this compound has a more stoichiometric concentration of Fe, Sn and O than those prepared by ball milling.