Jane Addams and Ellen Gates Starr opened Hull House, Chicago’s first settlement house, in 1889 as a means of confronting poverty, poor housing conditions, disease, discouragement, and other ills that flourished in the predominately immigrant Halstead neighborhood. Because Hull House volunteers lived at the House, in the center of the community, they were well-equipped to respond knowledgeably to the neighborhood conditions. Hull House residents worked for reform in areas such as education, labor, juvenile protection, immigration, welfare, housing, and suffrage and they provided the community with a plethora of activities and services during the Progressive Era. As the community expressed their needs, Hull House volunteers responded to them. This dissertation provides evidence that social activism did not just take the form of political engagement and occupational health efforts but that it also included disease and illness prevention efforts. An examination of activist work of the Hull House Woman’s Club helps create an understanding of the intersection of activism and disease and illness prevention, and how activists used strategies to improve the health and wellbeing of people at the turn of the century. Specifically, three groups of women—the neighborhood women, the club women, and public health knowledge-holders—came together to address public health issues in the Nineteenth Ward. Each of these three groups played an integral role in the success of Hull House public health activism; it was their coming together that enabled them to create such powerful change. This dissertation specifically examines the women’s efforts in 1894 to improve garbage collection and sanitation and their 1902 efforts to eliminate typhoid in their neighborhood. This dissertation argues that, despite a lack of formal public health education or training, Woman’s Club members utilized local knowledge to improve health conditions in the Nineteenth Ward in Chicago. Woman’s Club activists acquired public health knowledge and developed activist strategies and techniques inductively, through trial and error, as they were carrying out their activist work. This dissertation helps fill in the historical gaps by exploring the strategies Hull House volunteers used to prevent disease and illness prevention.

Cette thèse est composée de deux parties dans lesquelles nous étudions d'une part des estimations d'erreurs pour des schémas numériques associés à des équations de Hamilton-Jacobi du premier ordre. D'autre part, nous nous intéressons a l'étude de la stabilité et de la contrôlabilité exacte frontière indirecte des équations d'onde couplées.Dans un premier temps, en utilisant la technique de Crandall-Lions, nous établissons une estimation d'erreur d'un schéma numérique monotone aux différences finies pour des conditions de jonction dites a flux limité, pour une équation de Hamilton-Jacobi du premier ordre. Ensuite, nous montrons que ce schéma numérique peut être généralisé à des conditions de jonction générales. Nous établissons alors la convergence de la solution discrétisée vers la solution de viscosité du problème continu. Enfin, nous proposons une nouvelle approche, à la Crandall-Lions, pour améliorer les estimations d'erreur déjà obtenues, pour une classe des Hamiltoniens bien choisis. Cette approche repose sur l'interprétation du type contrôle optimal de l'équation de Hamilton-Jacobi considérée.Dans un second temps, nous étudions la stabilisation et la contrôlabilité exacte frontière indirecte d'un système monodimensionnel d’équations d'ondes couplées. D'abord, nous considérons le cas d'un couplage avec termes de vitesses, et par une méthode spectrale, nous montrons que le système est exactement contrôlable moyennant un seul contrôle à la frontière. Les résultats dépendent de la nature arithmétique du quotient des vitesses de propagation et de la nature algébrique du terme de couplage. De plus, ils sont optimaux. Ensuite, nous considérons le cas d'un couplage d'ordre zéro et nous établissons un taux polynômial optimal de la décroissance de l'énergie. Enfin, nous montrons que le système est exactement contrôlable moyennant un seul contrôle à la frontière / The aim of this work is mainly to study on the one hand a numerical approximation of a first order Hamilton-Jacobi equation posed on a junction. On the other hand, we are concerned with the stability and the exact indirect boundary controllability of coupled wave equations in a one-dimensional setting.Firstly, using the Crandall-Lions technique, we establish an error estimate of a finite difference scheme for flux-limited junction conditions, associated to a first order Hamilton-Jacobi equation. We prove afterwards that the scheme can generally be extended to general junction conditions. We prove then the convergence of the numerical solution towards the viscosity solution of the continuous problem. We adopt afterwards a new approach, using the Crandall-Lions technique, in order to improve the error estimates for the finite difference scheme already introduced, for a class of well chosen Hamiltonians. This approach relies on the optimal control interpretation of the Hamilton-Jacobi equation under consideration.Secondly, we study the stabilization and the indirect exact boundary controllability of a system of weakly coupled wave equations in a one-dimensional setting. First, we consider the case of coupling by terms of velocities, and by a spectral method, we show that the system is exactly controllable through one single boundary control. The results depend on the arithmetic property of the ratio of the propagating speeds and on the algebraic property of the coupling parameter. Furthermore, we consider the case of zero coupling parameter and we establish an optimal polynomial energy decay rate. Finally, we prove that the system is exactly controllable through one single boundary control