Teses / dissertações sobre o tema "Équations aux dérivées partielles et ordinaires"
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Vilmart, Gilles. "Méthodes numériques géométriques et multi-échelles pour les équations différentielles (in English)". Habilitation à diriger des recherches, École normale supérieure de Cachan - ENS Cachan, 2013. http://tel.archives-ouvertes.fr/tel-00840733.
Texto completo da fonteAyed, Ibrahim. "Neural Models for Learning Real World Dynamics and the Neural Dynamics of Learning". Electronic Thesis or Diss., Sorbonne université, 2022. http://www.theses.fr/2022SORUS434.
Texto completo da fonteThe work presented in this thesis was initially motivated by the discrepancy between the impressive performances of modern neural networks and the lack of applications to scientific problems for which data abounds. Focusing on evolution problems which are classically modelled through ordinary or partial differential equations~(O/PDEs) naturally brought us to consider the more general problem of representing and learning such equations from raw data with neural networks. This was the inception of the first part of our work. The point of view considered in this first part has a natural counterpart: what about the dynamics induced by the trajectories of the NN's weights during training or by the trajectories of data points within them during inference? Can they be usefully modelled? This question was the core of the second part of our work and, while theoretical tools other than O/PDEs happened to be useful in our analysis, our reasoning and intuition were fundamentally driven by considerations stemming from a dynamical viewpoint
Ouaari, Amel. "Modèles paramétriques de processus de branchement uni et multi-types". Thesis, Montpellier, 2018. http://www.theses.fr/2018MONTS109/document.
Texto completo da fonteThis thesis aims to propose parametric models for single and multi-type branching processes. The importance of the theory of branching processes is pointed out. Hence, developing various tools and specific concepts in several domains is important for applications. For those purpose, we recall some definitions and results of the single-and-multi-type branching processes theory in discrete and continuous case. Afterward, we focus on the methodological development of those models.In the second part, the evolution of a single population in the continuous case has been studied. Then, some parametric distribution families associated to particular branching mechanisms are explored. Recursive computational procedure and relevant properties concerning the associted probability distributions are derived from generating functions that satisfy specified linear partial differential equations. The suggested families are useful for the modeling of systems that are more coherent with population dynamics, contrarily to the usual hypothesis of Poisson distributions, that cannot be argued.In the third part, the evolution of different populations with interaction is explored. Similarly, some parametric models of homogeneous multi-type branching processes in continuous time are proposed. Afterwards, we consider a particular model where an autonomous donor parent population feeds in individuals, K types progeny populations that interacts. This model is well adapted to the study of dynamical systems of populations in interaction. This simple model, but has a rich variety of behaviors.The study of such systems is also done regarding the evolution of generating functions of multidimensional ndividual countrings. To achievea such study, ordinary and partial differential equations are used to establish the implicit equations of temporal and multidimensional distributions. Analytical and numerical methods for equation resolution are then discussed, and examples of particular models are developed.In conclusion, the relevancy of this approach is argumed, censidering parameters interpretation in the development of inference methods for the various applied domains
Kurbatova, Polina. "Modélisation hybride de l'érythropoïèse et des maladies sanguines". Phd thesis, Université Claude Bernard - Lyon I, 2011. http://tel.archives-ouvertes.fr/tel-00752835.
Texto completo da fonteVilmart, Gilles. "Étude d'intégrateurs géométriques pour des équations différentielles". Phd thesis, Université Rennes 1, 2008. http://tel.archives-ouvertes.fr/tel-00348112.
Texto completo da fonteDans la première partie, on introduit une nouvelle approche de construction d'intégrateurs numériques géométriques d'ordre élevé en s'inspirant de la théorie des équations différentielles modifiées. Le cas des méthodes développables en B-séries est spécifiquement analysé et on introduit une nouvelle loi de composition sur les B-séries. L'efficacité de cette approche est illustrée par la construction d'un nouvel intégrateur géométrique d'ordre élevé pour les équations du mouvement d'un corps rigide. On obtient également une méthode numérique précise pour le calcul de points conjugués pour les géodésiques du corps rigide.
Dans la seconde partie, on étudie dans quelle mesure les excellentes performances des méthodes symplectiques, pour l'intégration à long terme en astronomie et en dynamique moléculaire, persistent pour les problèmes de contrôle optimal. On discute également l'extension de la théorie des équations modifiées aux problèmes de contrôle optimal.
Dans le même esprit que les équations modifiées, on considère dans la dernière partie des méthodes de pas fractionnaire (splitting) pour les systèmes hamiltoniens perturbés, utilisant des potentiels modifiés. On termine par la construction de méthodes de splitting d'ordre élevé avec temps complexes pour les équations aux dérivées partielles paraboliques, notamment les problèmes de réaction-diffusion en chimie.
Kurbatova, Polina. "Modélisation hybride de l’érythropoïèse et des maladies sanguines". Thesis, Lyon 1, 2011. http://www.theses.fr/2011LYO10258/document.
Texto completo da fonteThis dissertation is devoted to the development of new methods of mathematical modeling in biology and medicine, off-lattice discrete-continuous hybrid models, and their applications to modelling of hematopoiesis and blood disorders, such as leukemia and anemia. In this approach, biological cells are considered as discrete objects while intracellular and extracellular networks are described with continuous models, ordinary or partial differential equations. Cells interact mechanically and biochemically between each other and with the surrounding medium. They can divide, die by apoptosis or differentiate. Their fate is determined by intracellular regulation and influenced by local control from the surrounding cells or by global regulation from other organs. In the first part of the thesis, hybrid models with off-lattice cell dynamics are introduced. Model examples specific for biological processes and describing competition between cell proliferation and apoptosis, proliferation and differentiation and between cell cycling and quiescent state are investigated. Biological pattern formation with hybrid models is discussed. Application to bacteria filament is illustrated. In the next chapter, hybrid model are applied in order to model erythropoiesis, red blood cell production in the bone marrow. The model includes immature blood cells, erythroid progenitors, which can self-renew, differentiate or die by apoptosis, more mature cells, reticulocytes, which influence erythroid progenitors by means of growth factor Fas-ligand, and macrophages, which are present in erythroblastic islands in vivo. Intracellular and extracellular regulation by proteins and growth factors are specified and the feedback by the hormones erythropoietin and glucocorticoids is taken into account. The role of macrophages to stabilize erythroblastic islands is shown. Comparison of modelling with experiments on anemia in mice is carried out. The following chapter is devoted to leukemia modelling and treatment. Erythroleukemia, a subtype of Acute Myeloblastic Leukemia (AML), develops due to insufficient differentiation of erythroid progenitors and their excessive slef-renewal. A Physiologically Based Pharmacokinetics-Pharmacodynamics (PBPKPD) model of leukemia treatment with AraC drug and chronotherapeutic treatments of leukemia are examined. Comparison with clinical data on blast count in blood is carried out. The last chapter deals with the passage from a hybrid model to a continuous model in the 1D case. A convergence theorem is proved. Numerical simulations confirm a good agreement between these approaches
Duminil, Sébastien. "Extrapolation vectorielle et applications aux équations aux dérivées partielles". Phd thesis, Université du Littoral Côte d'Opale, 2012. http://tel.archives-ouvertes.fr/tel-00790115.
Texto completo da fonteDiop, Mamadou Abdoul. "Equations aux dérivées partielles stochastiques et homogénéisation". Aix-Marseille 1, 2003. http://www.theses.fr/2003AIX11017.
Texto completo da fonteThis thesis is devoted to some problems connected to the theory of homogenization of random parabolic operators with large potential. It is assumed that the said operators have a periodic spatial microstructure whose characteristics are rapidly oscillating stationary random process in time. Two different cases of non diffusive scaling are addressed. Namely, the case when the oscillation in time is faster than that in spatial variables and the opposite case when the time oscillation is slower than that the spatial one. It is shown that in the former case, under certain mixing conditions,the corresponding Cauchy problem admits homogenization and its solution converges in probability to a solution of a deterministic semilinear operator. In the latter case the limit equation is a stochastic partial differential equation. Here a solution of the original Cauchy problem converges in law in the energy functional space, while con vergence in probability does not takes place. The thesis consists of an introduction and three different parts. In the introduction we give an elementary presentation of the basic ideas in the homogenization theory. The first chapter, deals with the results contained in this thesis. In the second chapter the operators with Markov driving processes are considered. In the second part the operators with non Markov coefficients are investigated
Sow, Ahmadou Bamba. "Approche probabiliste et homogénéisation d'équations aux dérivées partielles". Aix-Marseille 1, 2005. http://www.theses.fr/2005AIX11046.
Texto completo da fonteSellami-Omrani, Sonia. "Equations aux dérivées partielles non-linéaires et ondes progressives". Paris 6, 1993. http://www.theses.fr/1993PA066641.
Texto completo da fonteGrimberg, Gérard Emile. "D'Alembert et les équations aux dérivées partielles en hydrodynamique". Paris 7, 1998. http://www.theses.fr/1998PA070116.
Texto completo da fonteDhersin, Jean-Stéphane. "Super-mouvement brownien, serpent brownien et équations aux dérivées partielles". Paris 6, 1997. http://www.theses.fr/1997PA066065.
Texto completo da fonteMerlet, Benoît. "Sur quelques équations aux dérivées partielles et leur analyse numérique". Paris 11, 2004. http://www.theses.fr/2004PA112162.
Texto completo da fonteIn this thesis, four Partial Differential Equations of different nature are studied, numerically or/and theoretically. The first part deals with non-conservative hyperbolic systems in one space dimension. In the case of non-conservative hyperbolic systems, several definitions of shock waves exist in the literature, in this paper, we propose and study a new, very simple one in the case of genuinely non-linear fields. The second part is concerned with the Harmonic Map flow. We build solutions to the harmonic map flow from the unit disk into the unit sphere which have constant degree, in a co-rotational symmetric frame. First we prove the existence of such solutions, using a time semi-discrete scheme then we compute numerically these solutions by a moving-mesh method which allows us to deal with the singularities. The third part deals with the initial-and-boundary value problem for the Kadomtse-Petviashvili II equation posed on a strip with a Dirichlet left boundary condition and two kinds of conditions on the right boundary. Moreover we treat the case of the half plane and we show a result of convergence. In the last part, we investigate by numerical means a conjecture proposed by Guy David about the existence of a new Global Minimizer for the Mumford-Shah Functional in R^3. We are led to study a spectral problem for the Laplace operator with Neumann boundary conditions on a two dimensional subdomain of the sphere S^2 with reentrant corners. In particular, we have to compute the first eigenvector of this operator and accurate approximations of the singular coefficients of this eigenvector at each corner. For that we use the Singular Complement Method
Moussaoui, Hadjer. "Contribution aux équations différentielles stochastiques rétrogrades et application aux équations aux dérivées partielles et au contrôle stochastique". Electronic Thesis or Diss., Toulon, 2018. http://www.theses.fr/2018TOUL0016.
Texto completo da fonteThe objective of this thesis is to study backward stochastic differential equations (BSDE) and forward-backward stochastic differential equations (FBSDE), the main results are:The first is about the solvability of logarithmic BSDE of type (lylllnlyll lzlJllnlzll) and application to partial differential equations (PDE). The second concems the existence of strict optimal control for a system driven by a strongly coupled FBSDE. Multiple applications are established. A result of existence and uniqueness of the solution of the Hamilton-Jacobi-Belmann equation (HJB) is also established
Perez, Sylvie. "Identification et homogénéisation de paramètres dans des équations aux dérivées partielles". Pau, 1999. http://www.theses.fr/1999PAUU3016.
Texto completo da fonteJoukovskaïa, Tatiana. "Singularités de minimax et solutions faibles d'équations aux derivées partielles". Paris 7, 1994. http://www.theses.fr/1994PA077046.
Texto completo da fonteBaudouin, Lucie. "Problèmes inverses et commande robuste de quelques équations aux dérivées partielles". Habilitation à diriger des recherches, Université Paul Sabatier - Toulouse III, 2014. http://tel.archives-ouvertes.fr/tel-01067485.
Texto completo da fonteNouaili, Nejla. "Théorèmes de Liouville et singularités dans les équations aux dérivées partielles". Paris 6, 2008. http://www.theses.fr/2008PA066643.
Texto completo da fonteRivière, Olivier. "Equations différentielles stochastiques progressives rétrogrades couplées : équations aux dérivées partielles et discrétisation". Paris 5, 2005. http://www.theses.fr/2005PA05S028.
Texto completo da fonteThis thesis deals with the forward backward stochastic differential equations, in particular those with a coefficient of progressive diffusion which depends on all unknowns of the problem. We propose an original way to get onto this subject, letting us to reobtain some classical results of existence and uniqueness in the spirit of Pardoux-Tang and Yong's results, and to find a probabilistic representation of a new class of parabolic PDE, in which derivation coefficient of order 2 depends on the gradient of the solution. We also propose an iterative discretization scheme. We prove its convergence and give an evaluation of the error on a particular example
Bartier, Jean-Philippe. "Méthode d'entropie et comportement asymptotique des solutions d'équations paraboliques linéaires et non-linéaires". Paris 9, 2005. https://portail.bu.dauphine.fr/fileviewer/index.php?doc=2005PA090070.
Texto completo da fonteGuichard, Frédéric. "Axiomatisation des analyses multi-échelles d'images et de films". Paris 9, 1994. https://portail.bu.dauphine.fr/fileviewer/index.php?doc=1994PA090010.
Texto completo da fontePiozin, Lambert. "Quelques résultats sur les équations rétrogrades et équations aux dérivées partielles stochastiques avec singularités". Thesis, Le Mans, 2015. http://www.theses.fr/2015LEMA1004/document.
Texto completo da fonteThis thesis is devoted to the study of some problems in the field of backward stochastic differential equations (BSDE), and their applications to partial differential equations.In the first chapter, we introduce the notion of backward doubly stochastic differential equations (BDSDE) with singular terminal condition. A first work consists to study the case of BDSDE with monotone generator. We then obtain existing result by an approximating scheme built considering a truncation of the terminal condition. The last part of this chapter aim to establish the link with stochastic partial differential equations, using a weak solution approach developed by Bally, Matoussi in 2001.The second chapter is devoted to the BSDEs with singular terminal conditions and jumps. As in the previous chapter the tricky part will be to prove continuity in T. We formulate sufficient conditions on the jumps in order to obtain it. A section is then dedicated to establish a link between a minimal solution of our BSDE and partial integro-differential equations.The last chapter is dedicated to doubly reflected second order backward stochastic differential equations (2DRBSDE). We have been looking to establish existence and uniqueness for such equations. In order to obtain this, we had to focus first on the upper reflection problem for 2BSDEs. We combined then these results to those already existing to give a well-posedness context to 2DRBSDE. Uniqueness is established as a straight consequence of a representation property. Existence is obtained using shifted spaces, and regular conditional probability distributions. A last part is then consecrated to the link with some Dynkin games and Israeli options
Xia, Bo. "Equations aux dérivées partielles et aléas". Thesis, Université Paris-Saclay (ComUE), 2016. http://www.theses.fr/2016SACLS171/document.
Texto completo da fonteIn this thesis, we consider a wave equation. We first showed that the equation is almost sure global well-posed via Bourgain’s high-low frequency decomposition under the regularity assumption s > 2(p−3)/(p−1). Then we lowered down this regularity requirement to be (p−3)/(p−1) by invoking a probabilistic a priori estimate. We also consider approximation of the above achieved solutions by smooth solutions and the stability of this approximating procedure. And we concluded that this equation is everywhere ill-posed in the super-critical regime. Next, we considered the quintic beam equation on 3D torus. And we showed that this equation is almost sure global well-posed in certain super-critical regime. Lastly, we proved that the image measure of the Gaussian measure under the generalized BBM flow map satisfies a log-Sobolev type inequality with a little bit loss of integrability
Riviere, Olivier. "Equations différentielles stochastiques progressives rétrogrades couplées : équations aux dérivées partielles et discrétisation". Phd thesis, Université René Descartes - Paris V, 2005. http://tel.archives-ouvertes.fr/tel-00011231.
Texto completo da fonteLissy, Pierre. "Sur la contrôlabilité et son coût pour quelques équations aux dérivées partielles". Phd thesis, Université Pierre et Marie Curie - Paris VI, 2013. http://tel.archives-ouvertes.fr/tel-00918763.
Texto completo da fonteXu, Mingyu. "Contributions à l'étude des équations différentielles stochastiques rétrogrades fléchies et applications aux équations et dérivées partielles". Le Mans, 2005. http://cyberdoc.univ-lemans.fr/theses/2005/2005LEMA1004.pdf.
Texto completo da fonteIn the first chapter, we consider the reflected backward stochastic differential equation (BSDEsin short) with one or two right continuous and left limited (RCLL in short) barriers. Using the Picarditeration method, we obtained the existence and uniqueness of the solution of the reflected BSDEwith two RCLL barriers. Then we use the penalization method to the case of one RCLL barrier. Considering the solutions (Y n,Zn,Kn) of penalized equations as solutions of reflected BSDEs,we prove that the limit (Y,Z,K) is the solution of equation, by properties of Snell envelope andmonotonic limit theorem (Peng S. , 1999). In the case of equation with two RCLL barriers, by theanalogue method, we prove the limit (Y,Z,K) of penalized equation is the solution of problem,by the representation of solutions via Dynkin game. Here we need a generalized monotonic limittheorem, which permit us to pass the limit for penalized equations. In a second work, we have generalized this type of result to the case where barriers are just inL2, by the method of penalization and the theory of g-supersolution. In the second chapter, we consider the reflected BSDEs with one continuous barrier, associatedto (_, f,L), when _ 2 L2(FT ), f(t, !, y, z) is continuous, satisfies monotonic and general increasingconditions on y, and Lipschitz condition on z, and when the barrier (Lt)0_t_T is a progressivelymeasurable continuous process, which verifies certain integrability condition. We have also notable prove the existence and uniqueness of solution in L2, for this reflectedequation with determinist terminal time. The proof of existence is effected by four steps. The firststep consists to prove the result under the boundness condition of _, f(t, 0) et L+. The second step(the most delicate) consists to relax the boundness condition of L+ ; the following two step permitus to obtain the general result, relaxing the boundness condition on _ and f(t, 0). The comparisontheorems play important roles, which help us to pass the limit in the equations. Then we study thecase when the terminal time is a stopping time. The existence and uniqueness of the solution arealso proved. In the third chapter, we have studied the reflected BSDEs with one barrier, whose generator fsatisfies the monotonic and general increasing condition on y, and quadratic and linear condition onz, when the barrier L is uniformly bounded. We prove the existence of a solution by approximation,under these conditions. We also find a necessary and sufficient condition for the case f(t, !, y, z) =|z|2, and construct its solution explicitly. For the case f(t, !, y, z) = |z|p, p 2 (1, 2), we prove asufficient condition. In the forth chapter, we treat the reflected BSDE with two barrier, when f satisfies the mono-tonic, continuous and general increasing conditions on y, and Lipschitz condition on z, like in thesecond chapter. For the barriers, we suppose that L and U are continuous, L < U on [0, T], andMokoboski condition. We prove the existence and uniqueness of the solution for this equation. In the fifth chapter, we study the applications of BSDE. A important application of BSDEconsists to give a probabilistic interpretation (nonlinear Feynman-Kac formula) pour solutions ofsemilinear parabolic partial differential equations. We apply the approximation method and resultsof BSDE in (Pardoux, 1999) for semiliear PDE in Sobolev sense, by the solution of correspondingBSDEs. In following, we use the notion of PDE with obstacle (Bally et al. , 2004). By the sameapproximation in second chapter, we prove the probabilistic interpretation of the solution (u, _) ofPDE by the solution (Y,Z,K) of reflected BSDE. Here, we suppose that the obstacle h is polynomialincreasing. We prove a theorem which permits us to replace the regular test function by the randomtest function under monotonic and general increasing conditions, and by this theorem we obtainthe uniqueness of the solution of PDE from the solution of BSDE or reflected BSDE. Finally, in the last chapter, we study the numerical solutions of BSDEs and present somesimulation results, and we apply this technique to the calculation of American option
Debbi, Latifa. "Equations aux dérivées partielles déterministes et stochastiques avec opérateurs fractionnaires". Nancy 1, 2006. http://www.theses.fr/2006NAN10046.
Texto completo da fonteThis thesis treats application of fractional calculus in stochastic analysis. In the first part, the definition of the the multidimensional Riesz-Feller fractional differential operator is extended to higher order. The operator obtained generalizes several known fractional differential and pseudodifferential operators. High order fractional Fokker-Plank equations are studied in both the probabilistic and the quasiprobabilistic approaches. In particular, the solutions are represented via stable Lévy processes and generalization of Airy's function. In the second part, onedimensional stochastic fractional partial differential equations perturbed by space-time white noise are considered. The existence and the uniqueness of field solutions and of L2solutions are proved under different Lipschtz conditions. Spatial and temporal Hölder exponents of the field solutions are obtained. Further, equivalence between several definitions of L2solutions is proven. In particular, Fourier transform is used to give meaning to some stochastic fractional partial differential equations
Gueye, Mamadou. "Contrôlabilité pour quelques équations aux dérivées partielles : contrôles insensibilisants et contrôle d'équations dégénérées". Paris 6, 2013. http://www.theses.fr/2013PA066410.
Texto completo da fonteOur work is a contribution to the theoretical study of some controllability problemsarising in fluid mechanics and various applied mathematics fields. We mainly focus on thecontrollability of Navier-Stokes type systems with fewer scalar controls. In Chapter 2, weinvestigate the existence of insensitizing controls for the Navier-Stokes system. We firstprove the null controllability for a linearized problem, using known Carleman estimates. Then, we work in special weighted functional classes to apply an inverse mapping theorem. In Chapter 3, we have managed to prove the same insensitivity results with a controlhaving at most two non zero components. We proved new Carleman estimates withparticular observation terms for this purpose. In Chapter 4, the results are extended tothe Boussinesq system with two vanishing components. The idea is to transpose the resultsof Chapter 3 to a more complex example. In Chapter 5, we investigate the exact controllability of linear parabolic and hyperbolicequations which degenerate at one end of the interval on which they are posed. First, weconsider the corresponding class of degenerate hyperbolic equations. Then, we prove sharpobservability estimates for these equations using non-harmonic Fourier series. We get thecontrollability of the degenerate parabolic equations using a transmutation method
Mauffrey, Karine. "Contrôlabilité de systèmes gouvernés par des équations aux dérivées partielles". Phd thesis, Université de Franche-Comté, 2012. http://tel.archives-ouvertes.fr/tel-00864091.
Texto completo da fonteJouannelle, Olivier. "Une étude comparative entre des schémas numériques 2D et splitting pour des e. D. P hyperboliques non linéaires bidimensionnelles dans le cadre des fonctions généralisées". Antilles-Guyane, 2010. https://hal.archives-ouvertes.fr/tel-01487366.
Texto completo da fonteThis work is devoted to the theoritical research and to the numerical calculus of weak solutions (in the sens of generalized functions) for the non linear transport equation8u 8f(u) 8g(u)8t (x,y,t) +a(x,y,t)-ax(x,y,t) +b(x,y,t)fiij(x,y,t) = °pour t > 0with the initial condition u(x, y, 0) = uo(x, y) where the functions {(x, y, t) --;. A(x, y, tn and {(x, y, t) --;. B(x, y, tn belong to L00 (R2 X R+) (but can be discontinuous), the functions f and g are smooth and monotonous, the function ((x,y) --;. Uo(x,yn belongs to Loo(JR2). We recall the necessary notions on nonlinear generalized functions for introducing their tensorial product. The main results (to determine the weak solutions) are sufficient conditions so that, when a sum of generalized functions (like Heaviside or Dirac products) is associated with zero, each terms of the sum is equal to zero. Thanks to these theoretical results, we can solve the Riemann problem with the help of a solver written like tensorial product of Heaviside functions (or like a sum of tensorial product of Heaviside functions) in order to obtain the weak solutions. These weak solutions allow to develop two dimensional numerical Godunov type schemes. Then, numerical tests are performed which give a comparison between the results obtained by these 2D schemes and the ones of the splitting method. These tests prove that the 2D numerical schemes are as reliable as the ones obtained by splitting. They are also more simple in their expression. Moreover, a more detailed comparative study of the two types of numerical schemes show that the 2D schemes are far less expensive in the linear case as well as in the non linear case. They are stable for the LOO norm, unlike the splitting schemes
Salazar, Wilfredo. "Contribution aux équations aux dérivées partielles non linéaires et non locales et application au trafic routier". Thesis, Rouen, INSA, 2016. http://www.theses.fr/2016ISAM0016/document.
Texto completo da fonteThis work deals with the modelling, analysis and numerical analysis of non- linear and non-local partial differential equations and their application to traffic flow. Traffic can be simulated at different scales. Mainly, we have the microscopic scale which describes the dynamics of each of the vehicles individually and the macroscopic scale which describes the traffic as a fluid using macroscopic quantities such as the density of vehicles and the average speed. In this PhD thesis, using the theory of viscosity solutions, we derive macroscopic models from microscopic models. The interest of these results is that microscopic models are very intuitive and easy to manipulate to describe a particular situation (bifurcation, a traffic light,...), however, they are not adapted for big simulations (to simulate the traffic in an entire city for example). Conversely, macroscopic models are less easy to modify (to simulate a particular situation) but they can be used for big simulations. The idea is then to find the macroscopic model equivalent to a microscopic model describing a particular scenario (a junction, a bifurcation, different types of drivers, a school zone,...). The first part of this work contains an homogenization result and a numerical homogenization result for a microscopic model with different types of drivers. The second part contains an homogenization and numerical homogenization result for microscopic models with a local perturbation (a moderator, a school zone,...). Finally, we present an homogenization result for a bifurcation
Laurent, Camille. "Contrôle d'équations aux dérivées partielles non linéaires dispersives". Phd thesis, Université Paris Sud - Paris XI, 2010. http://tel.archives-ouvertes.fr/tel-00536082.
Texto completo da fonteDeaconu, Madalina. "Processus stochastiques et équations aux dérivées partielles : applications des espaces de Besov aux processus stochastiques". Nancy 1, 1997. http://www.theses.fr/1997NAN10046.
Texto completo da fonteThe first part of this thesis contains topics relating stochastic processes to partial differential equations via the stochastic differential equation. We prove first the convergence in law to the stationary distribution for a non-linear process, reflected in [-1, 1]. Two such stationary densities are computed and numerical results are presented. Further, we describe the behaviour of the hitting times for a strongly inward real diffusion. We consider next sorne reflected Brownian motions in the unit disk and we compute the maximum of the expectation of the time spent by this process in the disk. The second part of this work is devoted to sorne applications of Besov spaces to stochastic processes. We treat at the beginning the membership of the iterated Brownian motion to Besov and Besov-Orlicz spaces. We examine next the Besov regularity for a two indexed stochastic process, solution of the Walsh equation. The last application presents the approximation of a function in the d-dimensional cube by tensor product neural networks
Moisan, Lionel. "Traitement numérique d'images et de films : équations aux dérivées partielles préservant forme et relief". Paris 9, 1997. https://portail.bu.dauphine.fr/fileviewer/index.php?doc=1997PA090055.
Texto completo da fonteCollion, Stephane. "Fonctions critiques et équations aux dérivées partielles elliptiques sur les variétés riemanniennes compactes". Phd thesis, Université Pierre et Marie Curie - Paris VI, 2004. http://tel.archives-ouvertes.fr/tel-00007685.
Texto completo da fonteBoudin, Laurent. "Etude mathématique des équations aux dérivées partielles cinétiques et hyperboliques de la physique". Orléans, 2000. http://www.theses.fr/2000ORLE2031.
Texto completo da fonteIn this work, we investigate some problems coming from fluid mechanics which are modelled by partial differential equations (PDE)
Colin, Thierry. "Problème de Cauchy et effets régularisants pour des équations aux dérivées partielles dispersives". Cachan, Ecole normale supérieure, 1993. http://www.theses.fr/1993DENS0003.
Texto completo da fonteCollion, Stéphane. "Fonctions critiques et équations aux dérivées partielles elliptiques sur les variétés riemanniennes compactes". Paris 6, 2004. https://tel.archives-ouvertes.fr/tel-00007685.
Texto completo da fonteGao, Yueyuan. "Méthodes de volumes finis pour des équations aux dérivées partielles déterministes et stochastiques". Thesis, Université Paris-Saclay (ComUE), 2015. http://www.theses.fr/2015SACLS187/document.
Texto completo da fonteThis thesis bears on numerical methods for deterministic and stochastic partial differential equations; we perform numerical simulations by means of finite volume methods and prove convergence results.In Chapter 1, we apply a semi-implicit time scheme together with the generalized finite volume method SUSHI for the numerical simulation of density driven flows in porous media; it amounts to solve a nonlinear convection-diffusion parabolic equation for the concentration coupled with an elliptic equation for the pressure. We then propose a numerical scheme to simulate density driven flows in porous media coupled to heat transfer. We use adaptive meshes, based upon square or cubic volume elements.In Chapter 2, We perform Monte-Carlo simulations in the one-dimensional torus for the first order Burgers equation forced by a stochastic source term with zero spatial integral. We suppose that this source term is a white noise in time, and consider various regularities in space. We apply a finite volume scheme combining the Godunov numerical flux with the Euler-Maruyama integrator in time. It turns out that the empirical mean converges to the space-average of the deterministic initial condition as t → ∞. The empirical variance also stabilizes for large time, towards a limit which depends on the space regularity and on the intensity of the noise.In Chapter 3, we study a time explicit finite volume method with an upwind scheme for a first order conservation law with a monotone flux function and a multiplicative source term involving a Q-Wiener process. We present some a priori estimates including a weak BV estimate. After performing a time interpolation, we prove two entropy inequalities for the discrete solution and show that it converges up to a subsequence to a stochastic measure-valued entropy solution of the conservation law in the sense of Young measures.In Chapter 4, we obtain similar results as in Chapter 3, in the case that the flux function is non-monotone, and that the convection term is discretized by means of a monotone scheme
Grillot, Philippe. "Singularités isolées dans des équations et des systèmes elliptiques semi-linéaires". Tours, 1997. http://www.theses.fr/1997TOUR4007.
Texto completo da fontePrevost, Céline. "Applications des équations aux dérivés partielles aux problèmes de dynamique des populations et traitement numérique". Orléans, 2004. http://www.theses.fr/2004ORLE2072.
Texto completo da fonteTalbi, Mouloud. "Résolution stochastique d'équations aux dérivées partielles paraboliques à coefficients discontinus et applications physiques". Paris 6, 1987. http://www.theses.fr/1987PA066638.
Texto completo da fonteSchorsch, Julien. "Contributions à l’estimation paramétrique des modèles décrits par les équations aux dérivées partielles". Doctoral thesis, Université de Lorraine, Nancy, France, 2013. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/245203.
Texto completo da fonteWang, Hao. "Equations différentielles stochastiques rétrogrades réfléchies et applications au problème d'investissement réversible et aux équations aux dérivées partielles". Le Mans, 2009. http://cyberdoc.univ-lemans.fr/theses/2009/2009LEMA1013.pdf.
Texto completo da fonteThe main objective of the thesis is to study the existence and uniqueness of solutions of reflected backward stochastic differential equations and to relate this notion to the study of the problems such as the reversible investment or so-called optimal switching problem, the mixed zero-sum stochastic differential games and the probabilistic interpretation of the weak solution of partial differential equations, either in viscosity sense or in Sobolev space under different framework
Plazanet, Philippe. "Contributions à l'analyse des fonctions convexes et des différences de fonctions convexes : application à l'optimisation et à la théorie des E.D.P". Toulouse 3, 1990. http://www.theses.fr/1990TOU30202.
Texto completo da fonteGarnier, Jimmy. "Analyse mathématique de modèles de dynamique des populations : équations aux dérivées partielles paraboliques et équations intégro-différentielles". Phd thesis, Aix-Marseille Université, 2012. http://tel.archives-ouvertes.fr/tel-00755296.
Texto completo da fonteFilipe, Margarida. "Étude mathématique et numérique d'un problème d'interaction fluide-structure dépendant du temps par la méthode de couplage éléments finis-équations intégrales". Palaiseau, Ecole polytechnique, 1994. http://www.theses.fr/1994EPXX0035.
Texto completo da fonteSamson, Christophe. "Contribution à la classification d'images satellitaires par approche variationnelle et équations aux dérivées partielles". Phd thesis, Université de Nice Sophia-Antipolis, 2000. http://tel.archives-ouvertes.fr/tel-00319709.
Texto completo da fonteMacherey, Arthur. "Approximation et réduction de modèle pour les équations aux dérivées partielles avec interprétation probabiliste". Thesis, Ecole centrale de Nantes, 2021. http://www.theses.fr/2021ECDN0026.
Texto completo da fonteIn this thesis, we are interested in the numerical solution of models governed by partial differential equations that admit a probabilistic interpretation. In a first part, we consider partial differential equations in high dimension. Based on a probabilistic interpretation of the solution which allows to obtain pointwise evaluations of the solution using Monte-Carlo methods, we propose an algorithm combining an adaptive interpolation method and a variance reduction method to approximate the global solution. In a second part, we focus on reduced basis methods for parametric partial differential equations. We propose two greedy algorithms based on a probabilistic interpretation of the error. We also propose a discrete optimization algorithm probably approximately correct in relative precision which allows us, for these two greedy algorithms, to judiciously select a snapshot to add to the reduced basis based on the probabilistic representation of the approximation error
Pacard, Frank. "Existence et compacité de solutions de certaines équations aux dérivées partielles elliptiques non-linéaires". Paris 11, 1991. http://www.theses.fr/1991PA112151.
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