http://hdl.handle.net/10174/265 2026-04-04T10:49:24Z http://hdl.handle.net/10174/40555 Title: Effet de la diffusion saturante sur les équations hyperboliques Authors: Maypaokha, Gnord Abstract: In this thesis, we study the effect of the saturating diffusion on the hyperbolic equations. We begin by studying the general Cauchy problem of the hyperbolic equation perturbed with the saturating diffusion. We establish the convergence of the corresponding solutions to the entropy weak solution of the hyperbolic conservation law. Then we consider the diffusivedispersive perturbation by adding a linear dispersion. We establish some relevant estimates of the solutions of the new problem. These latter seem not sufficient to prove the convergence in the vanishing regularisation limit. Therefore, we focus on the special solutions depending on one variable, called the travelling wave solutions. The problem reduces to a second-order ordinary differential equation that we can study through a phase plane analysis. Numerical simulations are developed to show the behaviour of the travelling waves. We also determine numerically the minimal value of the diffusion coefficient for which the perturbed problem has monotone travelling waves, and we classify the wave profiles into three different types: monotone, with a finite number of oscillations, and with infinite oscillations. We prove many theoretical results that confirm the numerical observations. Finally, based on the results of the travelling waves, we formulate conjectures about the convergence of the regularised solutions to the entropy weak solution of the hyperbolic conservation law as the diffusion and dispersion parameters tend to zero. 2025-12-15T00:00:00Z http://hdl.handle.net/10174/40547 Title: Analyse mathématique de modèles structurés de maladies hydriques: application au Laos Authors: Doungsavanh, Bouasy Abstract: In this thesis, we introduced an innovative model that integrates spatial interactions between humans and snails, along with an in-depth analysis of the prevalence of schistosomiasis in humans. Our primary objective is to demonstrate the existence of a monotone wave of propagation linking an unstable endemic equilibrium to a stable disease-free equilibrium. The results show that for schistosomiasis to spread, the propagation speed of the disease must exceed that of the water flow. Next, we focus on coupling the schistosomiasis model with the Saint-Venant equation. We establish the well-posedness and positivity of the solution. Our observations reveal that the speed of the water has a greater influence on the situation than depth. In low-flow areas, shallow depth contributes to the concentration of schistosomiasis by creating favorable conditions for snails and the survival of the parasite. In the final chapter, we develop a compartmental model that takes into account the life cycle of the schistosome and three types of definitive hosts: humans, carabaos, and rodents, to describe the situation in Lake Mainit. The main objective is to determine the optimal control strategy to reduce the prevalence of schistosomiasis. The study demonstrates that mechanical and aquatic controls, while beneficial, are insufficient on their own to interrupt transmission. We recommend a comprehensive and integrated control strategy that combines chemotherapy, mechanical measures, and aquatic interventions. 2025-12-12T00:00:00Z http://hdl.handle.net/10174/12521 Title: Equações diferenciais estocásticas na modelação do crescimento individual em ambiente aleatório Authors: Filipe, Patrícia A. Abstract: Este estudo centra-se na análise de modelos de crescimento individual em ambiente aleatório. Para tal, foram descritos modelos mais gerais de equações diferenciais estocásticas. Apresentamos o caso em que existe uma unica forma funcional para descrever a din^amica m edia da curva de crescimento completa e generalizamos para o caso multif asico, em que consideramos que o coe ciente de crescimento assume valores diferentes para diferentes fases da vida do indivíduo. Desenvolvemos também o caso em que o tamanho médio assimptótico varia aleatoriamente de indivíduo para indivíduo. S~ao estudados os tópicos de estimação e previsão. Caracterizamos o tempo que um indivíduo demora a atingir um determinado tamanho. Quando se trata de um tamanho de interesse económico, podemos destacar a importância destes resultados e, neste contexto, são abordados problemas de optimização. Os resultados e métodos são ilustrados utilizando dados do peso de bovinos Mertolengos. 2011-07-28T23:00:00Z http://hdl.handle.net/10174/5055 Title: Modelling and Performance Evaluation of Mobile Ad Hoc Networks Authors: Jacinto, Gonçalo Abstract: Mobile ad hoc networks are characterized by having nodes that are self-organized and cooperative without any kind of infrastructure, being the most promising upgrade of the current telecommunication systems. The mobility and multihop capability of these networks allows the network topology to change rapidly and unpredictably, turning necessary the development of appropriate models to describe the multihop connectivity and the dynamic of multihop paths. The research carried on in this dissertation starts by addressing the multihop connectivity for one-dimensional and two-dimensional ad hoc networks. The hop count probability distributions are derived when the underlying node spatial distribution is drawn from a Poisson process and, by using a Poisson randomization technique, when a fixed number of relay nodes are uniformly distributed in a region of interest. Numerical results illustrate the computation of the hop count probabilities. We then present an analytical framework to characterize the random behavior of a multihop path by means of a piecewise deterministic Markov process. The mean path duration and the path persistence metrics are obtained as the unique solution of a system of integro-differential equations, and a recursive scheme for their computation is provided. Numerical results are presented to illustrate the computation of the metrics and to compare the associated results with independent link approximation results 2011-02-28T00:00:00Z