Dans cette thèse, nous étudions des modèles mathématiques concernant certains problèmes d'écoulement de fluide à densité variable. Le premier chapitre résume l'ensemble de la thèse et se concentre sur les résultats obtenus, la nouveauté et la comparaison avec la littérature existante. Dans le deuxième chapitre, nous étudions la stabilisation locale des équations non homogènes de Navier-Stokes dans un canal 2d autour du flot de Poiseuille. Nous concevons un contrôle feedback de la vitesse qui agit sur l'entrée du domaine de sorte que la vitesse et la densité du fluide soient stabilisées autour du flot de Poiseuille, à condition que la densité initiale soit donnée par une constante additionnée d'une perturbation dont le support se situe loin du bord latéral du canal. Dans le troisième chapitre, nous étudions un système couplant les équations de Navier-Stokes compressibles à une structure élastique située à la frontière du domaine fluide. Nous prouvons l'existence locale de solutions solides pour ce système couplé. Dans le quatrième chapitre, notre objectif est d'étudier la nulle- contrôlabilité d'un problemè d'interaction fluide-structure linéarisé dans un canal bi dimensional. L'écoulement du fluide est ici modélisé par les équations de Navier-Stokes compressibles. En ce qui concerne la structure, nous considérons une poutre de type Euler-Bernoulli amortie située sur une partie du bord. Dans ce chapitre, nous établissons une inégalité d'observabilité pour le problème considéré d'interaction fluid-structure linéarisé qui constitue le premier pas vers la preuve de la nulle contrôlabilité du système. / In this thesis we study mathematical models concerning some fluid flow problems with variable density. The first chapter is a summary of the entire thesis and focuses on the results obtained, novelty and comparison with the existing literature. In the second chapter we study the local stabilization of the non-homogeneous Navier-Stokes equations in a 2d channel around Poiseuille flow. We design a feedback control of the velocity which acts on the inflow boundary of the domain such that both the fluid velocity and density are stabilized around Poiseuille flow provided the initial density is given by a constant added with a perturbation, such that the perturbation is supported away from the lateral boundary of the channel. In the third chapter we prove the local in time existence of strong solutions for a system coupling the compressible Navier-Stokes equations with an elastic structure located at the boundary of the fluid domain. In the fourth chapter our objective is to study the null controllability of a linearized compressible fluid structure interaction problem in a 2d channel where the structure is elastic and located at the fluid boundary. In this chapter we establish an observability inequality for the linearized fluid structure interaction problem under consideration which is the first step towards the direction of proving the null controllability of the system.

Dans cette thèse nous adressons le problème de commande des véhicules marins sous-actionnés. La motivation clé de ce sujet de recherche vient du fait qui les systèmes sous-actionnés posent des défis aussi bien théoriques et pratiques pour l'ingénieur automaticien. En fait, ces systèmes ne peuvent pas être stabilisés par des commandes lisses invariantes dans le temps. De plus, en dépit du nombre de méthodes disponibles pour la commande des systèmes mécaniques sous-actionnés, peu ont adressé des points pratiques importantes tels que l'inclusion explicite de dynamique dans la formulation de problème de commande et le besoin de faire face aux perturbations environnementales résultants des courants des vagues, par exemple. Cette thèse attaque certains de ces problèmes, formule et résout les problèmes de commande de positionnement dynamique, de la poursuite de trajectoire et du suivie de chemin des véhicules marins sous-actionnés. La première partie de cette thèse (Chapitres 3 et 4) constituent les éléments théoriques fondamentaux pour l'analyse du modèle et la synthèse des commandes pour les véhicules marins sous-actionnés. Particulièrement, nous montrons au chapitre 3 que le modèle de véhicule marin sous-actionné ne satisfait pas la condition de nécessaire Brockett pour la stabilisation des systèmes nonlinéaires par actions continues et invariantes dans le temps. Cependant, Il sera montré qu'il est possible d'atteindre la stabilisation en utilisant une commande discontinue ou variable dans le temps. Le chapitre 4 consiste à appliquer des résultats récents sur les systèmes cascades nonlinéaires pour résoudre le problème de déterminer des lois de commande qui stabilisent à l'origine la position et l'orientation d vaisseau sous-actionnés. Deux transformations sont introduites pour représenter le système dans une forme de cascade. Par quelques propriétés du modèle, nous montrons en premier que la stabilisation globale et asymptotique du système se réduit a stabiliser une forme en chaîne de troisième ordre. Une approche discontinue par backstepping est ensuite employée pour la stabilisation du système de forme en chaîne via un retour d'état partiel. Nous montrons que la loi de commande proposée stabilise exponentiellement le modèle réduit dans un ensemble défini, assurant le stabilisation asymptotique, local et uniforme du modèle de vaisseau marin sous-actionné. Pour assurer la stabilité uniforme globale cependant, un backstepping et le temps combinés variant l'approche de contrôle est donc employée. Prochain, nous exploitons la structure de cascade pour construire une trajectoire convenable produite par les équations dynamiques d'un véritable sous-actionnés bateau. Nous montrons ensuite que la stabilisation globale peut être assurée par une par une combinaison de la commande par backstepping et une commande variable dans le temps. Ensuite nous abordons le problème de poursuite de trajectoire. Dans lequel la trajectoire de référence est générée par un navire sous-actionné virtuel. Nous montrons ensuite qu'il existe une commande qui force exponentiellement le navire à la poursuite de la trajectoire partant d'une condition initiale quelconque. Utilisant une approche des Systems cascades, nous montrons que la dynamique de l'erreur de poursuite peut être vue comme une cascade d'un système linéaire et d'un système en chaine de deuxième ordre. La deuxième partie de cette thèse (Chapitre 5, 6 et 7) est consacrée au problème de la manoeuvre du vaisseau sous-actionné le long d'un chemin désiré avec une dynamique prescrite. La conception de la loi de commande est abordée par deux approches. La première vient d'une observation qu'il est plausible en pratique de manoeuvrer le véhicule tel qu'il soit sur son chemin de référence est que sa vitesse totale soit tangente au chemin. Il sera aussi supposé que le véhicule voyage le long du chemin avec une vitesse directe constante. La seconde approche ne conditionne pas la vitesse directe pour être constante. Dans le Chapitre 5, nous exploitons l'approche abordée pour le suivi de chemin pour résoudre le problème de coordinations d'un groupe de véhicules marins. Il est objet de manoeuvrer le mouvement de chaque véhicule tel que le mouvement du groupe est prescrit par un comportement désiré. Ainsi, le mouvement indépendant est coordonné comme une formation selon le comportement désirée. Dans ce chapitre nous considérerons le problème de formation ou plusieurs véhicules sont synchronisés de manière qu'ils soient commandés comme une formation de structure virtuelle. Le chapitre 6, est dévouée au problème général de la commande par retour de sortie pour la stabilisation globale des véhicules marins sous-actionnés. Une application de tel observateur est ensuite faite au problème de la poursuite de trajectoire d'un vaisseau sous-actionné.

偏見不只影響遭受者的身心健康，也違背社會正義，為了改善這樣的狀況，研究者們致力於發展降低偏見的方案。不過這些降低偏見的方案通常針對種族或性別群體，卻甚少關心肥胖者與愛滋感染者。肥胖者、愛滋感染者不僅受研究社群忽視，他們在生活中亦不受重視（如醫療體系），因此本論文著眼降低人們對肥胖者、愛滋感染者的偏見。研究一發展降低偏見方案，透過撰寫支持肥胖者或愛滋感染者的短文，引發人們言行不一的認知失調感，可能進而改變其原本對肥胖者或愛滋感染者的偏見。研究一的結果顯示，只有撰寫愛滋主題的參與者其愛滋偏見分數低於其他組別，也就是說他們的行為違反本身對愛滋感染者的既有態度而產生認知失調，透過降低愛滋偏見來化解認知失調之不適感。不過，撰寫肥胖主題的參與者，其肥胖偏見分數則與各組無異，也就是說這種降低偏見的方案對肥胖者的偏見無影響。預試二發現，相對於愛滋感染者，肥胖者通常被視為較可控制自己身屬於該社會群體的命運（可控制性），且其較需為自己的遭遇負責。為了檢視人們認為肥胖者與愛滋感染者可控制性的差異，是否影響偏見方案的效果，研究二除了改良研究一的降低偏見方案外，更操弄可控制性的高低。研究二發現可控制性會調節降低偏見方案的效果－當人們認為成為愛滋感染者是自己可以控制時，降低偏見方案的效果較弱；反之，若人們認為成為愛滋感染者是自己不能控制的，則降低偏見的效果較強。不過，撰寫肥胖主題文章的參與者則無此效果。這樣的差異或許是因為人們對肥胖者與愛滋感染者的熟悉程度有所不同。相較於愛滋感染者，人們對肥胖者較為熟悉，對其態度不容易改變，不論是接受高可控或低可控的訊息操弄，都無法改變人們對肥胖者的想法。根據本論文結果，認知失調適合降低人們較不熟悉與視其較為不可控的社會群體，如愛滋感染者，不適合應用在人們較熟悉的社會群體，如肥胖者。本論文進一步討論降低偏見方案執行困難的原因，並提出可能的建議與後續的研究方向。 / Prejudice and discrimination may have negative consequences on subordinate group members’ physical and mental health, and prejudice and discrimination also violate social justice. To deal with these problems, researchers have dedicated to develop various interventions to counter prejudice and discrimination. However, most of these interventions focus on racial and gender minorities, and researchers largely ignore people with obesity and people with HIV/AIDS. The purpose of this thesis is to develop an intervention that could reduce prejudice against people with obesity, as well as to reduce prejudice against people with HIV/AIDS. According to cognitive dissonance theory, when people’s attitudes and behavior are inconsistent, they feel uncomfortable and in turn change their attitudes to eliminate the inconsistency (Festinger, 1957). Following the basic ideas in cognitive dissonance theory, in Study 1, I randomly assigned participants to write presumably counter-attitudinal essays, in which they write about people with obesity or people with HIV/AIDS (to advocate allocating more resources to them), or school policy change (a control group). The results showed that after writing about people with HIV/AIDS, participants displayed significantly lower prejudice against people with HIV/AIDS than participants in other conditions. However, after writing about people with obesity, participants’ prejudice against people with obesity remained at similar levels as participants in other conditions. According to findings in the second pilot study, the diverging findings in Study 1 may be due to that people with obesity were considered having more controllability and responsibility than people with HIV/AIDS. To further explore the effects of levels of controllability on intervention, I revised Study 1’s intervention and added a manipulation of controllability on people with obesity or on people with HIV/AIDS. The findings showed that controllability manipulation moderated the intervention effect on people with HIV/AIDS, but had no effect on people with obesity. Because participants were more familiar with people with obesity than with people with HIV/AIDS, it is possible that attitudes toward a familiar social group are more difficult to be changed than the attitudes toward an unfamiliar social group, The results suggested that interventions based on cognitive dissonance principle have effects on unfamiliar social groups, such as people with HIV/AIDS. Obstacles with prejudice reduction interventions were further discussed; suggestions and future research directions were offered.

本論文嘗試以行為引發機制與行為抑制機制的觀點，探討非法且屬人際層面的男性攻擊行為，從中評估常表現攻擊行為個體的認知、情緒與行為缺陷。由於攻擊行為的特殊性，個體表現攻擊行為時，相關的行為機制包括表現該行為可能得到獎賞的行為引發機制﹔表現該行為可能得到懲罰的行為抑制機制﹔與攻擊他人時，被害者的非語文訊息引發的個體的暴力抑制機制。研究一根據暴力抑制機制的理論內容發展實驗工具，透過違反道德與違反慣例圖片組的呈現，了解高、中、低攻擊組的表現差異。結果發現高攻擊組對兩違反情境的嚴重程度評估較低，同時，在違反道德圖片組刺激下，高攻擊組表現較少的道德情緒與較少的同理行為。研究二則透過研究一發展的圖片組評估個體的暴力抑制機制運作能力，並結合Patterson與Newman的四階段理論發展實驗刺激，透過情境的操弄，了解高攻擊組之行為引發機制與行為抑制機制運作情形。結果發現經由兩套理論(暴力抑制機制與四階段理論)的結合，可將高攻擊組分為兩類，一類為暴力抑制機制運作正常，但行為引發機制運作過強﹔另一類為暴力抑制機制無法運作者。以認知、情緒與行為缺陷評估兩類高攻擊行為者發現，具有認知、情緒與行為缺陷的高攻擊行為者只有第二類。 / Based on a behavioral activation mechanism and two behavioral inhibition mechanisms, unlawful and interpersonal male aggression was studied. Moreover, the possibility of individuals’ cognitive, emotional, and behavioral deficiencies was evaluated. Due to the special quality of aggressive behavior, when a person acts aggressively, there will be three processes involved. They are the behavioral activation mechanism activated by reward, the behavioral inhibition mechanism induced by punishment, and the Violence Inhibition Mechanism (VIM) triggered by victims’ cues of distress. In order to study these three processes, two sets of pictures were developed from study 1 in order to evaluate how participants functioned their VIM. The results showed differences between High, Medium, and Low Aggression Group. The High Aggression Group evaluated incidents of moral/ conventional transgression less serious than the other two groups did. Also, they showed less moral emotions and less empathic behaviors than the other two groups did. Based on the sets of pictures developed from Study 1, a group of young offenders were divided into two groups based on their VIM functioning. Further, a survival game was developed from Patterson and Newman’s four-stage model. By manipulating situations to present reward/punishment, those young offenders showed different aggressive patterns. Young offenders with good VIM functioning behaved more aggressively when there were rewards. Relatively, young offenders with poor VIM functioning were less likely to be influenced by either reward or punishment. The implications were discussed in the article.

Made available in DSpace on 2014-12-17T15:48:12Z (GMT). No. of bitstreams: 1 CamilaA.pdf: 551643 bytes, checksum: c211e0d0bbaf86da86337efffe6f407b (MD5) Previous issue date: 2007-07-28 / The Reconfigurables Architectures had appeares as an alternative to the ASICs and the GGP, keeping a balance between flexibility and performance. This work presents a proposal for the modeling of Reconfigurables with Chu Spaces, describing the subjects main about this thematic. The solution proposal consists of a modeling that uses a generalization of the Chu Spaces, called of Chu nets, to model the configurations of a Reconfigurables Architectures. To validate the models, three algorithms had been developed and implemented to compose configurable logic blocks, detection of controllability and observability in applications for Reconfigurables Architectures modeled by Chu nets / As Arquiteturas Reconfigur?veis surgiram no ambiente acad?mico como uma alternativa aos ASICs e aos GGP, mantendo um equil?brio entre flexibilidade e performance. Este trabalho apresenta uma proposta para a modelagem de Arquiteturas Reconfigur?veis com Espa?os de Chu, descrevendo os principais assuntos relativos a esta tem?tica. A solu??o proposta consiste em uma modelagem que utiliza uma generaliza??o dos Espa?os de Chu, denominada de Chu nets, para modelar as configura??es de uma Arquitetura Reconfigur?vel. Como forma de validar os modelos, foram desenvolvidos e implementados tr?s algoritmos que realizam a composi??o de c?lulas l?gicas program?veis, detec??o dos vetores de controlabilidade e observabilidade em aplica??es para Arquiteturas Reconfigur?veis, que est?o modeladas atrav?s das Chu nets

Submitted by Johnny Rodrigues (johnnyrodrigues@ufcg.edu.br) on 2018-08-06T15:24:59Z No. of bitstreams: 1 LUCIANO CIPRIANO DA SILVA - DISSERTAÇÃO PPGMAT 2013..pdf: 1125916 bytes, checksum: d2b1ef64aa3ef95093acedfd0f7a711c (MD5) / Made available in DSpace on 2018-08-06T15:24:59Z (GMT). No. of bitstreams: 1 LUCIANO CIPRIANO DA SILVA - DISSERTAÇÃO PPGMAT 2013..pdf: 1125916 bytes, checksum: d2b1ef64aa3ef95093acedfd0f7a711c (MD5) Previous issue date: 2013-02 / Capes / Neste trabalho estudamos o controle hierárquico, para um sistema parabólico, em um domínio não cilíndrico. O controle hierárquico é um problema que consiste em aproximar, em um tempo fixado, as soluções das equações de estado que temos, (essas soluções dependem de funções chamadas controles), de um estado considerado ideal, através de um sistema de líder, que é o controle independente, e seguidores, que são os controles que dependem da ação do líder. Começamos fazendo uma transformação do problema original para um equivalente em domínio cilíndrico, então estudamos o controle hierárquico deste sistema. Usaremos a estratégia de Stackelberg-Nash, processo no qual, para cada escolha do líder, procuramos por seguidores que satisfaçam um certo problema de minimização, as soluções deste problema formam o que chamamos de Equilíbrio de Nash, resolvido esse problema, trabalhamos para provar que o sistema é aproximadamente controlável usando o líder. Resolvemos ainda um sistema sistema de otimalidade para os seguidores. / We present hierarchic control to a parabolic system in a noncylindrical domain. The hierarchic control is a problem that is how to bring in a fixed time, the solutions of the equations of state we have, (these solutions depend on a functions called controls), a state considered ideal, througha system of leading, independent control, and followers, the leader controls dependents. We start by making a transformation of the original problem to an equivalent cylindrical domain, then do the hierarchic control of this problem. We use the strategy Stackelberg-Nash, a process in which each leader’s choice, look for followers to satisfy a minimization problem, the solution of this problem form what we call the Nash equilibrium, solved this problem, work to prove that the approximately system is controllable using the leader. We further resolve to a of optimality for followers.

Submitted by Maike Costa (maiksebas@gmail.com) on 2016-03-28T14:37:42Z No. of bitstreams: 1 arquivototal.pdf: 2200397 bytes, checksum: fa2b77afd6348b68a616a33acb7c7cb2 (MD5) / Made available in DSpace on 2016-03-28T14:37:42Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 2200397 bytes, checksum: fa2b77afd6348b68a616a33acb7c7cb2 (MD5) Previous issue date: 2014-03-20 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / The aim of this thesis is to present some controllability results for some fluid mechanic models. More precisely, we will prove the existence of controls that steer the solution of our system from a prescribed initial state to a desired final state at a given positive time. The two first Chapters deal with the controllability of the Burgers-α and Leray-α models. The Leray-α model is a regularized variant of the Navier-Stokes system (α is a small positive parameter), that can also be viewed as a model for turbulent flows; the Burgers-α model can be viewed as a related toy model of Leray-α. We prove that the Leray-α and Burgers-α models are locally null controllable, with controls uniformly bounded in α. We also prove that, if the initial data are sufficiently small, the pair state-control (that steers the solution to zero) for the Leray-α system (resp. the Burgers-α system) converges as α → 0+ to a pair state-control(that steers the solution to zero) for the Navier-Stokes equations (resp. the Burgers equation). The third Chapter is devoted to the boundary controllability of inviscid incompressible fluids for which thermal effects are important. They will be modeled through the so called Boussinesq approximation. In the zero heat diffusion case, by adapting and extending some ideas from J.-M. Coron [14] and O. Glass [45], we establish the simultaneous global exact controllability of the velocity field and the temperature for 2D and 3D flows. When the heat diffusion coefficient is positive, we present some additional results concerning exact controllability for the velocity field and local null controllability of the temperature. In the last Chapter, we prove the local exact controllability to the trajectories for a coupled system of the Boussinesq kind, with a reduced number of controls. In the state system, the unknowns are: the velocity field and pressure of the fluid (y, p), the temperature θ and an additional variable c that can be viewed as the concentration of a contaminant solute. We prove several results, that essentially show that it is sufficient to act locally in space on the equations satisfied by θ and c. / O objetivo desta tese é apresentar alguns resultados controlabilidade para alguns modelos da mecânica dos fluidos. Mais precisamente, provaremos a existência de controles que conduzem a solução do nosso sistema de um estado inicial prescrito à um estado final desejado em um tempo positivo dado. Os dois primeiros Capítulos preocupam-se com a controlabilidade dos modelos de Burgers-α e Leray-α. O modelo de Leray-α é uma variante regularizada do sistema de Navier-Stokes (α é umparâmetro positivo pequeno), que pode também ser visto como um modelo de fluxos turbulentos; já o modelo Burgers-α pode ser visto como um modelo simplificado de Leray-α. Provamos que os modelos de Leray-α e Burgers-α são localmente controláveis a zero, com controles limitados uniformemente em α. Também provamos que, se os dados iniciais são suficientemente pequenos, o par estado-controle (que conduz a solução a zero) para o sistema de Leray-α (resp. para o sistema de Burgers-α) converge quando α → 0+ a um par estado-controle (que conduz a solução a zero) para as equações de Navier-Stokes (resp. para a equação de Burgers). O terceiro Capítulo é dedicado à controlabilidade de fluidos incompressíveis invíscidos nos quais os efeitos térmicos são importantes. Estes fluidos são modelados através da então chamada Aproximação de Boussinesq. No caso emque não há difusão de calor, adaptando e estendendo algumas idéias de J.-M. Coron [14] e O. Glass [45], estabelecemos a controlabilidade exata global simultaneamente do campo velocidade e da temperatura para fluxos em 2D e 3D. Quando o coeficiente de difusão do calor é positivo, apresentamos alguns resultados sobre a controlabilidade exata global para o campo velocidade e controlabilidade nula local para a temperatura. No último Capítulo, provamos a controlabilidade exata local à trajetórias de um sistema acoplado do tipo Boussinesq, com um número reduzido de controles. Nesse sistema, as incógnitas são: o campo velocidade e a pressão do fluido (y, p), a temperatura θ e uma variável adicional c que pode ser vista como a concentração de um soluto contaminante. Provamos vários resultados, que essencialmente mostram que é suficiente atuar localmente no espaço sobre as equações satisfeitas por θ e c.

Submitted by ANA KARLA PEREIRA RODRIGUES (anakarla_@hotmail.com) on 2017-08-23T16:00:02Z No. of bitstreams: 1 arquivototal.pdf: 9090532 bytes, checksum: d4fefb1d97e9c6d585d5d18a33abf752 (MD5) / Made available in DSpace on 2017-08-23T16:00:02Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 9090532 bytes, checksum: d4fefb1d97e9c6d585d5d18a33abf752 (MD5) Previous issue date: 2016-11-30 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this thesis we study controllability results, asymptotic behavior and inverse problem related to some problems of the theory of partial di erential equations. Two particular systems are the focus of the study: the Mindin-Timoshenko system, describing the vibrational motion of a plate or a beam, and the phase eld system describing the temperature and phase of a medium having two distinct physical states. The rst chapter is devoted to the study of the 1-D Mindlin-Timoshenko system with discontinuous coe cient. A Carleman inequality is obtained under the assumption of monotonicity on the beam speed. Subsequently, two applications are provided: the controllability of the control system acting on the boundary and Lipschitzian stability of the inverse problem of recovering a potential from a single measurement of the solution. In the second chapter we consider a contact problem characterized by the behavior of a two-dimensional plate whose board makes contact with a rigid obstacle. The formulation of this problem is presented by the 2-D Mindlin-Timoshenko system with boundary conditions and suitable damping terms. Concerning such system, is proved via penalty techniques, the existence of solution and that the system energy has exponential decay when the time approaches in nity. In the third chapter, the study is aimed at a nonlinear phase- eld system de ned in a real open interval. Here we present some controllability results when a single control acts, by means of Dirichlet conditions, on the temperature equation of the system on one of the endpoints of the interval. To prove the results is used the method of moments, plus a spectral study of operators associated to the system and xed point theory to deal with the nonlinearity. / Nesta tese estudamos resultados de controlabilidade, comportamento assintótico e problema inverso relacionados a alguns problemas da teoria de equações diferenciais parciais. Dois sistemas particulares são foco do estudo: o sistema de Mindin-Timoshenko, que descreve o movimento vibratório de uma placa ou viga, e o sistema de campo de fases que descreve a temperatura e a fase de um meio onde ocorrem dois estados físicos distintos. O primeiro capítulo é dedicado ao estudo do sistema de Mindlin-Timoshenko 1-D com coe ciente descontínuos. Uma desigualdade de Carleman é obtida sob a hipótese de monotonicidade sobre velocidade da viga. Posteriormente, são fornecidas duas aplicações: a controlabilidade do sistema com controles agindo na fronteira e a estabilidade Lipschitziana do problema inverso de recuperar um potencial através de uma única informação obtida sobre a solução. No segundo capítulo consideramos um problema de contato caracterizado pelo comportamento de uma placa bidimensional cujo bordo faz contato com um obstáculo rígido. A formulação deste problema é apresentada pelo sistema de Mindlin-Timoshenko 2-D com condi ções de fronteira e termos de amortecimento (damping) adequados. Sobre tal sistema, é provada, através de técnicas de penalização, a existência de solução e, posteriormente, que sua energia possui decaimento exponencial quando o tempo tende ao in nito. No terceiro capítulo o estudo é voltado a um sistema de campo de fases não-linear de nido em um intervalo aberto real. Neste espaço apresentamos alguns resultados de controlabilidade quando um único controle age, sob condições de Dirichlet, na equação da temperatura em um dos bordos do intervalo. Para provar os resultados é utilizado o método dos momentos, além de uma estudo espectral de operadores associados ao sistema e teoria de ponto xo para lidar com a não-linearidade.

Submitted by Leonardo Cavalcante (leo.ocavalcante@gmail.com) on 2018-05-03T13:44:12Z No. of bitstreams: 1 Arquivototal.pdf: 1150863 bytes, checksum: a7e25ab87986c9d088c0fe224303f97f (MD5) / Made available in DSpace on 2018-05-03T13:44:12Z (GMT). No. of bitstreams: 1 Arquivototal.pdf: 1150863 bytes, checksum: a7e25ab87986c9d088c0fe224303f97f (MD5) Previous issue date: 2017-03-31 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this thesis we presents results on the exact controllability of the partial Di erential Equations (PDEs) of the parabolic and hyperbolic type, in the context of hierarchic control, using the Stackelberg-Nash strategy. In every problems we consider a main control (leader) and two secondary controls (followers). To each leader we obtain a correnponding Nash equilibrium, associated to a bi-objective optimal control problem; then we look for a leader of minimal cost that solves the exact controllability problem. For the parabolic problems we have distributed and boundary controls, now in the hyperbolics every controls are distributed. We consider linear and semilinear cases, which we solve using observability inequality obtained combining right Carleman inequalities. Also we use a xed point method. / Nesta tese apresentamos resultados sobre controlabilidade exata de Equações Diferenciais Parciais (EDPs) dos tipos parabólico e hiperbólico, no contexto de controle hierárquico, usando a estratégia de Stackelberg-Nash. Em todos os problemas consideramos um controle principal (líder) e dois controles secundários (seguidores). Para cada líder obtemos um equil íbrio de Nash correspondente, associado a um problema de controle ótimo bi-objetivo; então buscamos o líder de custo que resolve o problema de controlabilidade. Para os problemas parabólicos temos controles distribuídos e na fronteira, já nos hiperbólico todos os controles são distribuídos. Consideramos casos lineares e semilineares, os quais resolvemos usando desigualdade de observabilidade obtidas combinando desigualdades de Carleman adequadas. Também usamos um método de ponto xo.

Neste trabalho, introduzimos os conceitos de controlabilidade e de observabilidade para equações diferenciais ordinárias generalizadas, apresentamos resultados inéditos sobre condições suficientes e necessárias para controlabilidade e para observabilidade para estas equações e também apresentaremos uma aplicação. Utilizando teoremas de correspondência entre equações diferenciais ordinárias generalizadas e outras equações diferenciais, traduzimos os resultados obtidos para os casos particulares de controlabilidade e observabilidade para equações diferenciais em medida e equações diferencias com impulsos. O fato de trabalharmos no ambiente das equações diferenciais ordinárias generalizadas permitiu que os resultados obtidos pudessem envolver funções com muitas descontinuidades e muito oscilantes, ou seja, de variação ilimitada. Os resultados novos apresentados aqui estão contidos no artigo [21] que se encontra em fase final de redação e será submetido à publicação em breve. / In this work, we introduce concepts of controllability and observability for generalized ordinary differential equations, we present new results on necessary and sufficient conditions for controllability and observability for these equations and we also present an application. Using theorems of correspondence between generalized ordinary differential equations and other differential equations, we translate the results obtained for the particular cases of controllability and observability for measure differential equations and differential equations with impulses. The fact that we work in the framework of generalized ordinary differential equations allows us to obtain results where the functions involved can have many discontinuities and be highly oscillating, that is, of unbounded variation. The new results presented here are contained in the preprint [21] which is under final revision and will soon be submitted for publication.