Na presente pesquisa estudamos o comportamento do sujeito pronominal no português uruguaio (PU) falado na região de fronteira entre Brasil e Uruguai (Santana do Livramento-Rivera). Associando alguns pressupostos da Teoria de Princípios e Parâmetros (CHOMSKY, 1981), mais especificamente o Parâmetro do Sujeito Nulo (pro-drop), e da Sociolinguística Variacionista (WEINREICH, LABOV e HERZOG, 1968), analisamos uma amostra de língua oral composta de falas de 37 informantes, investigando as seguintes questões: (1) no português uruguaio teríamos uma mudança linguística em curso no que se refere ao Parâmetro do Sujeito Nulo, de modo que ele venha a se tornar um sujeito pronominal pleno?; (2) quais são os fatores linguísticos e sociais condicionantes dessa produção e em que direção vai essa tendência, português brasileiro (PB) ou espanhol (E)? A análise dos fatores sociais e linguísticos selecionados permitiu observar que o PU também passa por um processo de mudança paramétrica, ainda que mais lenta, devido ao fato de estar submetido à pressão simultânea de duas línguas, e se apresenta como uma língua em que, em alguns contextos, a realização do sujeito pronominal é plena e, em outros, ainda conserva as características das línguas pro-drop. Confirma-se, ainda, que essa disputa não está terminada, embora haja indícios nos dados da geração mais nova de que as regras do espanhol vêm ganhando alguma força, talvez pela pressão da escola e dos meios de comunicação. Tudo indica, então, que a base do PU é o PB, porém algumas características do E estão presentes nesse aspecto da gramática. A análise realizada confirma a maior parte das hipóteses iniciais e dá indícios de que o PU e o PB poderiam configurar-se como duas línguas distintas, da mesma forma que o PB e o PE, como aponta Galves (1998), isto é, tudo parece indicar que, mesmo quando os enunciados superficialmente se parecem, a língua interna (Língua-I) seria diferente e os enunciados dos falantes teriam estatutos diferentes, algo que, no entanto, será necessário demonstrar com um outro modelo de coleta de dados, de natureza mais introspectiva. / In this research we study the behavior of the pronominal subject in the Uruguayan Portuguese language (PU) spoken in the border region between Brazil and Uruguay (Santana do Livramento-Rivera). Associating some assumptions from the Theory of Principles and Parameters (CHOMSKY, 1981), specifically the Null Subject Parameter (pro-drop), and from the Variationist Sociolinguistics (WEINREICH, LABOV and HERZOG, 1968), we analyze a sample of spoken language consisting of 37 informants, in order to investigate the following questions: (1) would we have in the Uruguayan Portuguese language a language change in progress with regard to the Null Subject Parameter, so that it will become a full pronominal subject? (2) what are the linguistic factors and social conditions of production and in which direction will this trend, Brazilian Portuguese (BP) or Spanish (E)? The analysis of social factors and selected language programs suggests that the PU is also undergoing a process of parametric change, albeit slower, due to the fact of being subjected to the pressure of two languages simultaneously, and is presented as a language that, in some contexts, the performance of the pronominal subject is full, and in others it still retains the characteristics of pro-drop languages. It is also confirmed that this dispute is not over, although there are indications in the data of the younger generation that the rules of Spanish are gaining some strength, maybe due to the pressure of school and the media. The analysis confirms most of our initial hypothesis and provides evidence that the PU and CP could be framed as two distinct languages, in the same way as the PB and PE, as appointed by GALVES (1998), that is, everything seems to indicate that, even when the statements superficially resemble, the internal language (Language I) would be different and the production of the speakers would have different statutes, something which, however, would just be demonstrated by means of another more introspective model of data collection.

In this work we study the existence of nontrivial weak solutions for some Hamiltonian elliptic systems in dimension two, involving a potential function and nonlinearities which possess maximal growth with respect to a critical curve (hyperbola). We consider four different cases. First, we study Hamiltonian systems in bounded domains with potential function identically zero. The second case deals with systems of equations on the whole space, the potential function is bounded from below for some positive constant and satisfies some integrability conditions, while the nonlinearities involve weight functions containing a singulatity at the origin. In the third case, we consider systems with coercivity potential functions and nonlinearities with weight functions which may have singularity at the origin or decay at infinity. In the last case, we study Hamiltonian systems, where the potential can be unbounded or can vanish at infinity. To establish the existence of solutions, we use variational methods combined with Trudinger-Moser type inequalities for Lorentz-Sobolev spaces and a finite-dimensional approximation. / Neste trabalho estudamos a existência de soluções fracas não triviais para sistemas hamiltonianos do tipo elíptico, em dimensão dois, envolvendo uma função potencial e não linearidades tendo crescimento exponencial máximo com respeito a uma curva (hipérbole) crítica. Consideramos quatro casos diferentes. Primeiramente estudamos sistemas de equações em domínios limitados com potencial nulo. No segundo caso, consideramos sistemas de equações em domínio ilimitado, sendo a função potencial limitada inferiormente por alguma constante positiva e satisfazendo algumas de integrabilidade, enquanto as não linearidades contêm funções-peso tendo uma singularidade na origem. A classe seguinte envolve potenciais coercivos e não linearidades com funções peso que podem ter singularidade na origem ou decaimento no infinito. O quarto caso é dedicado ao estudo de sistemas em que o potencial pode ser ilimitado ou decair a zero no infinito. Para estabelecer a existência de soluções, utilizamos métodos variacionais combinados com desigualdades do tipo Trudinger-Moser em espaços de Lorentz-Sobolev e a técnica de aproximação em dimensão finita.

Neste trabalho, estudamos a existência de soluções não triviais para uma classe de equações de Schrödinger não lineares envolvendo um campo magnético com condição de Dirichlet ou condição de fronteira mista Dirichlet-Neumann. Nos dois primeiros capítulos, damos uma estimativa para o número de soluções não triviais para o problema de Dirichlet em termos da topologia do domínio. Nos dois capítulos restantes, consideramos o problema de fronteira mista e estimamos o número de soluções não triviais em termos da topologia da porção da fronteira onde é prescrita a condição de Neumann. Em ambos os casos, usamos a teoria de categoria de Ljusternik-Schnirelmann e a teoria de Morse / We study the existence of nontrivial solutions for a class of nonlinear Schrödinger equations involving a magnetic field with Dirichlet or mixed DirichletNeumann boundary condition. In the first two chapters we give an estimate for the number of nontrivial solutions for the Dirichlet boundary value problem in terms of topology of the domain. In the last two chapters we consider mixed DirichletNeumann boundary value problems and the estimation of the number of nontrivial solutions is given in terms of the topology of the part of the boundary where the Neumann condition is prescribed. In both cases, we use Lyusternik- Shnirelman category and the Morse theory

L'impact sur le climat et sur la qualité de l'air des gaz émis par les activités humaines a de fortes retombées sociales et économiques. L'ozone (O3) troposphérique est produit à partir des polluants primaires comme les oxydes d'azote. Il est le troisième gaz par importance dans l'effet de serre après le dioxyde de carbone et le méthane, et il est l'un des polluants principaux pour ses effets oxydants sur les tissus organiques. Pour répondre au besoin de mesure continue de la concentration d'O3 plusieurs satellites emportent des sondeurs capables de mesurer leur signal dans les domaines ultra-violet, visible ou infrarouge du rayonnement terrestre. Le CNES développe notamment le sondeur infrarouge IASI à bord des satellites météorologiques polaires METOP. IASI, en orbite depuis de nombreuses années, permet d'estimer la concentration de certains gaz atmosphériques, notamment l'O3, avec une couverture spatio-temporelle jamais atteinte jusqu'à présent. Chaque jour IASI mesure le spectre infrarouge de l'atmosphère entre 650 et 2700 nm avec une résolution horizontale de 12 km, ce qui fait un volume de données géolocalisées de plusieurs dizaines de gigaoctets par jour. Ces observations constituent un jeu de données idéal pour la validation des modèles de chimie-transport (CTM) à la base des systèmes de surveillance et de prévision de la qualité de l'air. Ces modèles peuvent prendre en compte les observations satellitaires par une procédure mathématique appelée 'assimilation de données'. Cette technique permet de compléter l'information parfois parcellaire des satellites (par exemple à cause de la présence des nuages ou durant la nuit pour les capteurs UV-visible) et d'obtenir des champs 3D globaux des concentrations de certaines espèces chimiques avec une fréquence horaire. Dans ce contexte, il est très important de développer des algorithmes fiables et efficaces pour assimiler les données IASI dans les CTM. A cette fin, l'UMR/CECI (CERFACS) développe en collaboration avec le CNRM/Météo-France un outil d'assimilation (VALENTINA) pour le CTM MOCAGE ayant des applications à l'échelle globale ou régionale pour l'étude du climat ou de la qualité de l'air, notamment dans le cadre du projet européen Copernicus sur la composition de l'atmosphère (CAMS). Il collabore également avec le Laboratoire d'Aérologie, qui développe depuis plusieurs années l'algorithme SOFRID de restitution des profils verticaux d' O3 IASI basé sur le code de transfert radiatif RTTOV. Le travail de cette thèse concerne la mise au point et la production d'analyses d' O3 troposphérique tridimensionnelles par l'assimilation d'observations satellitaires (MLS, IASI) dans le CTM MOCAGE. L'objectif principal est de constituer une nouvelle base de données pour l'étude de la variabilité de l'ozone de l'échelle journalière à celle décennale. On démontre ainsi la capacité des analyses utilisant les données IASI à reproduire la réponse de l' O3 troposphérique à l'ENSO (El Niño Southern Oscillation) aux basses latitudes, apportant notamment des informations nouvelles sur la distribution verticale des anomalies associées. Une large part de ce travail a de plus consisté à analyser les biais entre les analyses et les données de sondages indépendantes. Une des raisons expliquant ces biais pourrait être l'utilisation d'a-priori et de covariances d'erreurs climatologiques fortement biaisés (notamment au niveau de la tropopause) dans la procédure d'inversion des produits d' O3 de IASI. Une seconde partie de la thèse a donc consisté à mettre en place une méthode permettant de prescrire des a-priori plus proches des situations réelles améliorant ainsi les profils d' O3 restitués. En conclusion cette thèse constitue une avancée significative vers l'amélioration des produits d' O3 troposphérique issus de l'instrument IASI, permettant d'envisager un suivi à long terme que le caractère opérationnel des satellites METOP facilitera. / Human activity produces gases impacting the climate and the air quality with important economic and social consequences. Tropospheric ozone (O3) is created by chemical reactions from primary pollutants as nitrogen oxides. O3 is the third most important greenhouse gas after carbon dioxide and methane. It is one of the most important pollutants due to its oxidant effects on biological tissue. Several sensors on board satellites measure ozone concentration in the Ultraviolet, visible, or in the Earth infrared radiance. The French national center for space studies CNES (Centre National d'Etudes Spatiales) has developed the infrared sounding IASI on board polar meteorological satellites METOP. IASI, in orbit for several years, has allowed to estimate concentration of atmospheric gases, particularly O3, with a spatio-temporal coverage never reached so far. Every day, IASI measures infrared spectrum of the atmosphere between 650 to 2700 nm with an horizontal resolution of 12 km, giving tens of Gigaoctet per day of geolocated data. These observations form a part of an ideal set of data for the Chemistry Transport Model (CTM). CTM are used to analyze and predict air quality and can take into account satellite data according to a mathematical procedure called 'data assimilation'. This technic allows to fill gaps in the satellite information (for instance due to clouds or during night for the UV-visible sensor) and to obtain 3D global fields of chemical species concentration on an hourly basis. Therefore, it is important to develop accurate and efficient algorithms to assimilate IASI data in the CTM's. To this end, the UMR/CECI (CERFACS) develops in collaboration with the CNRM/Météo-France an assimilation tool (named VALENTINA) to the CTM MOCAGE that has applications on global and regional scales for climate or air quality study. The CTM MOCAGE is part of the European Copernicus project on the atmospheric composition (CAMS). In addition, the UMR/CECI collaborates with the Laboratoire d'Aérologie that has developed for several years the SOFRID algorithm for the vertical profiles retrieval of IASI ozone data based on the radiative transfer code RTTOV. The study of this PhD includes the tridimensional production of tropospheric ozone analysis with data assimilation (MLS, IASI) in the CTM MOCAGE, and on the ozone variability. Hence, we demonstrate the analysis ability to reproduce tropospheric ozone in response to ENSO, by bringing new informations on the vertical structure of associated anomalies. The PhD also focuses on the study of biases between analyses and independent ozone soundings. One of the main reasons could be due to the use of the climatological a-priori and matrix error covariance associated, strongly biased (particularly around the tropopause) in the retrieval method of IASI ozone data. Therefore, the second part of the PhD has consisted implementation of a method that generates accurate a-priori to improve retrieved ozone profiles. As a conclusion, this PhD brings a significant progress towards the improvement of tropospheric ozone products from IASI instrument, that should contribute to the long-term monitoring of tropospheric ozone thanks to the operational nature of METOP satellites.

Condensação de Bose-Einstein é um fenômeno quântico que pode ser observado macroscopicamente. Para a sua obtenção são necessários aprisionamentos externos, porém a presença desses leva ao colapso da função de onda. As interações de longo alcance são propostas como uma forma alternativa ao confinamento externo, um vez que podem prevenir o colapso da função de onda. Neste trabalho será apresentada uma revisão sobre os estudos de condensados de Bose-Einstein. Também, será buscada a solução aproximada da equação de Schrödinger não linear e não-local, a qual descreve condensados de Bose-Einstein com auto-interações de longo alcance. Para isso, será suposta uma forma espacial da função de onda, permitindo o tratamento analítico do sistema dinâmico resultante. Ao fim, por meio do método variacional dependente do tempo, será demonstrado que existem soluções estáveis para a função de onda sujeito a interações de longo alcance na forma gaussiana e gravitacional. / Bose-Einstein condensation is a quantum phenomenon that can be observed macroscopically. External trappings are required to obtain them, however the presence of these leads to the collapse of the wave function. Long-range interactions are proposed as an alternative to external confinement, since they can prevent the collapse of the wave function. In this work a review will be presented on the Bose-Einstein condensate studies. Also, we review the approximate solution of the non-linear and non-local Schrödinger equation, which describes Bose-Einstein condensates with long-range auto-interactions. For this, a spatial form of the wave function will be assumed, allowing the analytical treatment of the system. Finally, through the time-dependent variational method, it will be demonstrated that there are stable solutions for the wave function subject to long-range interactions in gaussian and gravitational form.

Na presente pesquisa estudamos o comportamento do sujeito pronominal no português uruguaio (PU) falado na região de fronteira entre Brasil e Uruguai (Santana do Livramento-Rivera). Associando alguns pressupostos da Teoria de Princípios e Parâmetros (CHOMSKY, 1981), mais especificamente o Parâmetro do Sujeito Nulo (pro-drop), e da Sociolinguística Variacionista (WEINREICH, LABOV e HERZOG, 1968), analisamos uma amostra de língua oral composta de falas de 37 informantes, investigando as seguintes questões: (1) no português uruguaio teríamos uma mudança linguística em curso no que se refere ao Parâmetro do Sujeito Nulo, de modo que ele venha a se tornar um sujeito pronominal pleno?; (2) quais são os fatores linguísticos e sociais condicionantes dessa produção e em que direção vai essa tendência, português brasileiro (PB) ou espanhol (E)? A análise dos fatores sociais e linguísticos selecionados permitiu observar que o PU também passa por um processo de mudança paramétrica, ainda que mais lenta, devido ao fato de estar submetido à pressão simultânea de duas línguas, e se apresenta como uma língua em que, em alguns contextos, a realização do sujeito pronominal é plena e, em outros, ainda conserva as características das línguas pro-drop. Confirma-se, ainda, que essa disputa não está terminada, embora haja indícios nos dados da geração mais nova de que as regras do espanhol vêm ganhando alguma força, talvez pela pressão da escola e dos meios de comunicação. Tudo indica, então, que a base do PU é o PB, porém algumas características do E estão presentes nesse aspecto da gramática. A análise realizada confirma a maior parte das hipóteses iniciais e dá indícios de que o PU e o PB poderiam configurar-se como duas línguas distintas, da mesma forma que o PB e o PE, como aponta Galves (1998), isto é, tudo parece indicar que, mesmo quando os enunciados superficialmente se parecem, a língua interna (Língua-I) seria diferente e os enunciados dos falantes teriam estatutos diferentes, algo que, no entanto, será necessário demonstrar com um outro modelo de coleta de dados, de natureza mais introspectiva. / In this research we study the behavior of the pronominal subject in the Uruguayan Portuguese language (PU) spoken in the border region between Brazil and Uruguay (Santana do Livramento-Rivera). Associating some assumptions from the Theory of Principles and Parameters (CHOMSKY, 1981), specifically the Null Subject Parameter (pro-drop), and from the Variationist Sociolinguistics (WEINREICH, LABOV and HERZOG, 1968), we analyze a sample of spoken language consisting of 37 informants, in order to investigate the following questions: (1) would we have in the Uruguayan Portuguese language a language change in progress with regard to the Null Subject Parameter, so that it will become a full pronominal subject? (2) what are the linguistic factors and social conditions of production and in which direction will this trend, Brazilian Portuguese (BP) or Spanish (E)? The analysis of social factors and selected language programs suggests that the PU is also undergoing a process of parametric change, albeit slower, due to the fact of being subjected to the pressure of two languages simultaneously, and is presented as a language that, in some contexts, the performance of the pronominal subject is full, and in others it still retains the characteristics of pro-drop languages. It is also confirmed that this dispute is not over, although there are indications in the data of the younger generation that the rules of Spanish are gaining some strength, maybe due to the pressure of school and the media. The analysis confirms most of our initial hypothesis and provides evidence that the PU and CP could be framed as two distinct languages, in the same way as the PB and PE, as appointed by GALVES (1998), that is, everything seems to indicate that, even when the statements superficially resemble, the internal language (Language I) would be different and the production of the speakers would have different statutes, something which, however, would just be demonstrated by means of another more introspective model of data collection.

Neste trabalho, nós investigamos a estabilidade da solução trivial da seguinte Equação Diferencial em Medida (EDM) Dx = f(x, t) + g(x, t)Du, (1) onde \'B BARRA IND. c\' = {\'x PERTENCE A\' \'R POT. n\'; //x// \' < OU=\' c}, f : \'B BARRA IND.c\' × [a, b] \'SETA\' \'R POT.n\' e g : \'B BARRA IND. c\' × [a, b] \'SETA\' \' R POT n\', u : [a, b] \' ETA\' ! R é uma função de variação limitada em [a, b] e contínua à esquerda em (a, b], f(x, ·) é Lebesgue integrável em [a, b], g(x, ·) é du-integrável em [a, b], f(0, t) = 0 = g(0, t) para todo t e Dx e Du denotam as derivadas distribucionais de x e u no sentido de L. Schwartz. Nós consideramos as funções f e g num contexto bem geral. Assim, para obtermos nossos resultados, nós provamos a correspondência biunívoca entre as soluções da classe de EDMs (1) em tal contexto e as soluções de certa classe de equação diferencial ordinária generalizada (EDOG). Desta forma, foi possível aplicarmos as técnicas e resultados da teoria das equações diferenciais ordinárias generalizadas, como teoremas do tipo Lyapunov e do tipo Lyapunov inverso, para obtermos os resultados correspondentes para a EDM (1). Os resultados apresentados neste trabalho sobre estabilidade da solução trivial da EDM (1) são inéditos. Parte deles foram apresentados no 660 Seminário Brasileiro de Análise. Veja [7] / In this work, we investigate the stability of the trivial solution of the following Measure Differential Equation (MDE) Dx = f(x, t) + g(x, t)Du, (2) where \'B BARRA IND.c\' = {x \'PERTENCE A\' \'R POT.n\'; //x// \' < OU=\' c}, f : \'B BARRA IND.c\' × [a, b] \'SETA\' \'R POT.n\' and g : \'B BARRA IND.c\' × [a, b] \'SETA\' \'R POT. n\' , u is function of bounded variation in [a, b] which is also left continuous on (a, b], f(x, ·) is Lebesgue integrable in [a, b] and g(x, ·) is du-integrable in [a, b], f(0, t) = 0 = g(0, t) for all t and Dx, Du denote the derivatives of x and u in the sense of distributions of L. Schwartz. We consider the functions f and g in a general setting. Thus, in order to obtain our results, we prove there is a one-to-one correspondence between the solutions of the MDE 2) in this setting and the solutions of a certain class of generalized ordinary differential equation (GODE). In this manner, it was possible to apply the techniques and results from the teory of GODE\'s, such as Lyapunov-type and converse Lyapunov-type theorems, to obtain the corresponding results for our MDE (2). The results presented in this work concerning the stability of the trivial solution of the MDE (2) are new. Some of them were presented at the 66th Seminário Brasileiro de Análise. See [7]

Cette thèse traite du développement d'algorithmes d'estimation en haute dimension. Ces algorithmes visent à résoudre des problèmes de discrimination et de classification, notamment, en incorporant un mécanisme de sélection des variables pertinentes. Les contributions de cette thèse se concrétisent par deux algorithmes, GLOSS pour la discrimination et Mix-GLOSS pour la classification. Tous les deux sont basés sur le résolution d'une régression régularisée de type "optimal scoring" avec une formulation quadratique de la pénalité group-Lasso qui encourage l'élimination des descripteurs non-significatifs. Les fondements théoriques montrant que la régression de type "optimal scoring" pénalisée avec un terme "group-Lasso" permet de résoudre un problème d'analyse discriminante linéaire ont été développés ici pour la première fois. L'adaptation de cette théorie pour la classification avec l'algorithme EM n'est pas nouvelle, mais elle n'a jamais été détaillée précisément pour les pénalités qui induisent la parcimonie. Cette thèse démontre solidement que l'utilisation d'une régression de type "optimal scoring" pénalisée avec un terme "group-Lasso" à l'intérieur d'une boucle EM est possible. Nos algorithmes ont été testés avec des bases de données réelles et artificielles en haute dimension avec des résultats probants en terme de parcimonie, et ce, sans compromettre la performance du classifieur. / This thesis deals with the development of estimation algorithms with embedded feature selection the context of high dimensional data, in the supervised and unsupervised frameworks. The contributions of this work are materialized by two algorithms, GLOSS for the supervised domain and Mix-GLOSS for unsupervised counterpart. Both algorithms are based on the resolution of optimal scoring regression regularized with a quadratic formulation of the group-Lasso penalty which encourages the removal of uninformative features. The theoretical foundations that prove that a group-Lasso penalized optimal scoring regression can be used to solve a linear discriminant analysis bave been firstly developed in this work. The theory that adapts this technique to the unsupervised domain by means of the EM algorithm is not new, but it has never been clearly exposed for a sparsity-inducing penalty. This thesis solidly demonstrates that the utilization of group-Lasso penalized optimal scoring regression inside an EM algorithm is possible. Our algorithms have been tested with real and artificial high dimensional databases with impressive resuits from the point of view of the parsimony without compromising prediction performances.

<p>This thesis consists of four papers and a summary. The common topic of the included papers are the pricing equations of path-dependent options. Various properties of barrier options and American options are studied, such as convexity of option prices, the size of the continuation region in American option pricing and pricing formulas for turbo warrants. In Paper I we study the effect of model misspecification on barrier option pricing. It turns out that, as in the case of ordinary European and American options, this is closely related to convexity properties of the option prices. We show that barrier option prices are convex under certain conditions on the contract function and on the relation between the risk-free rate of return and the dividend rate. In Paper II a new condition is given to ensure that the early exercise feature in American option pricing has a positive value. We give necessary and sufficient conditions for the American option price to coincide with the corresponding European option price in at least one diffusion model. In Paper III we study parabolic obstacle problems related to American option pricing and in particular the size of the non-coincidence set. The main result is that if the boundary of the set of points where the obstacle is a strict subsolution to the differential equation is C¹-Dini in space and Lipschitz in time, there is a positive distance, which is uniform in space, between the boundary of this set and the boundary of the non-coincidence set. In Paper IV we derive explicit pricing formulas for turbo warrants under the classical Black-Scholes assumptions.</p>

This dissertation is concerned with the mathematical modeling of the flow in a porous cylinder with a focus on applications to solid rocket motors. After discussing the historical development and major contributions to the understanding of wall injected flows, we present an inviscid rotational model for solid and hybrid rockets with arbitrary headwall injection. Then, we address the problem of pressure integration and find that for a given divergence free velocity field, unless the vorticity transport equation is identically satisfied, one cannot find an analytic expression for the pressure by direct integration of the Navier-Stokes equations. This is followed by the application of a variational procedure to seek novel solutions with varying levels of kinetic energies. These are found to cover a wide spectrum of admissible motions ranging from purely irrotational to highly rotational fields. Subsequently, a second law analysis as well as an extension of Kelvin's energy theorem to open boundaries are presented to verify and corroborate the variational model. Finally, the focus is shifted to address the problem of laminar viscous flow in a porous cylinder with regressing walls. This is tackled using two different analytical techniques, namely, perturbation and decomposition. Comparisons with numerical Runge--Kutta solutions are also provided for a variety of wall Reynolds numbers and wall regression speeds.