Literatura científica selecionada sobre o tema "Systèmes faiblement hyperboliques"
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Teses / dissertações sobre o assunto "Systèmes faiblement hyperboliques"
Obata, Davi dos Anjos. "Ergodicité stable et mesures physiques pour des systèmes dynamiques faiblement hyperboliques". Thesis, Université Paris-Saclay (ComUE), 2019. http://www.theses.fr/2019SACLS488/document.
Texto completo da fonteIn this thesis we study the following topics:-stable ergodicity for conservative systems;-genericity of the existence of positive exponents for some skew products with two dimensional fibers;-rigidity of $u$-Gibbs measure for certain partially hyperbolic systems;-robust transitivity.We give a proof of stable ergodicity for a certain partially hyperbolic system without using accessibility. This system was introduced by Pierre Berger and Pablo Carrasco, and it has the following properties: it has a two dimensional center direction; it is non-uniformly hyperbolic having both a positive and a negative exponent along the center for almost every point, and the Oseledets decomposition is not dominated.In a different work, we find criteria of stable ergodicity for systems with a dominated splitting. In particular, we explore the notion of chain-hyperbolicity introduced by Sylvain Crovisier and Enrique Pujals. With this notion we give explicit criteria of stable ergodicity, and we give some applications.In a joint work with Mauricio Poletti, we prove that the random product of conservative surface diffeomorphisms generically has a region with positive exponents. Our results also hold for more general skew products.We also study dissipative perturbations of the Berger-Carrasco example. We classify all the $u$-Gibbs measures that may appear inside a neighborhood of the example. In this neighborhood, we prove that any $u$-Gibbs measure is either the unique SRB measure of the system or it has atomic disintegration along the center foliation. In a joint work with Pablo Carrasco, we prove that this example is robustly transitive (indeed robustly topologically mixing)
Morisse, Baptiste. "Le problème de Cauchy pour les systèmes quasi-linéaires faiblement hyperboliques ou non-hyperboliques en régularité Gevrey". Thesis, Sorbonne Paris Cité, 2017. http://www.theses.fr/2017USPCC188/document.
Texto completo da fonteWe consider the Cauchy problem for first-order, quasilinear systems of PDEs. In the initially elliptic case, that is when the principal symbol of the system has nonreal spectrum at time t=0, we prove an instability result in the sense of Hadamard. The proof is based on the construction of a family of exact solutions which exhib an exponential growth, both in time and frequency. That family leads to a defect of Hölder regularity of the flow, starting from evrey spaces to L² space. We prove analogous results for some cases of transition from hyperbolicity to ellipticity, with a potential restriction on the Gevrey index for which we may observe the instability. In a second time, we consider weakly hyperbolic systems. Thanks to an energy estimate in Gevrey spaces and the construction of a suitable symetriser, we prove local well-posedness for such a system. In doing so we use and prove a result on actions of pseudo-differential operators whose symbols have Gevrey regularity in the spatial variable
Dongmo, Nguepi Guissel Lagnol. "Modèles mathématiques et numériques avancés pour la simulation du polymère dans les réservoirs pétroliers". Electronic Thesis or Diss., université Paris-Saclay, 2021. http://www.theses.fr/2021UPASG077.
Texto completo da fonteAn effective technique to increase production in an oil field is to inject a mixture of water and polymer. The viscosity of polymer reduces the mobility of water, which then pushes oil better, resulting in a higher extraction rate. The numerical simulation of such an enhanced oil recovery is therefore of paramount importance. However, despite decades of research, the modeling of polymer flows in porous media and its numerical resolution remains a difficult subject.On the one hand, the models traditionally used by reservoir engineers exhibit, in the best case, resonance-like singularities that make them weakly hyperbolic. Thisdefect gives rise to some complications but remains acceptable. In the worst case, when we wish to incorporate the effect of the inaccessible pore volume (IPV), themodels become non-hyperbolic, which exacerbates the numerical instabilities that are likely to appear.On the other hand, classical numerical schemes do not yield satisfactory results. Without IPV, the excessive diffusion around the contact wave causes the most relevant information to be lost. With IPV, the existence of complex eigenvalues generates exponential instabilities at the continuous level that must be addressed at the discrete level to avoid a premature stop of the code.The objective of this thesis is to remedy these difficulties. Regarding models, we analyze several IPV laws and show an equivalence between two of them. Furthermore, we propose reasonable sufficient conditions on the IPV law to enforce weak hyperbolicity of the flow system. Regarding schemes for the problem without IPV, we advocate a correction to improve the accuracy of contact discontinuities. For the problem with IPV, we design a relaxation method that guarantees the stability of the calculations for all IPV laws
De, Chaisemartin Stéphane. "Modèles eulériens et simulation numérique de la dispersion turbulente de brouillards qui s'évaporent". Phd thesis, Ecole Centrale Paris, 2009. http://tel.archives-ouvertes.fr/tel-00443982.
Texto completo da fonteCrovisier, Sylvain. "Nombre de rotation et dynamique faiblement hyperbolique". Phd thesis, Université Paris Sud - Paris XI, 2001. http://tel.archives-ouvertes.fr/tel-00001185.
Texto completo da fonteGhedamsi, Mouna. "Solutions globales régulières pour quelques systèmes d'évolution". Paris 6, 2002. http://www.theses.fr/2002PA066489.
Texto completo da fonteFougeirol, Jérémie. "Structure de variété de Hilbert et masse sur l'ensemble des données initiales relativistes faiblement asymptotiquement hyperboliques". Thesis, Avignon, 2017. http://www.theses.fr/2017AVIG0417/document.
Texto completo da fonteGeneral relativity is a gravitational theory born a century ago, in which the universe is a 4-dimensional Lorentzian manifold (N,gamma) called spacetime and satisfying Einstein's field equations. When we separate the time dimension from the three spatial ones, constraint equations naturally follow on from the 3+1 décomposition of Einstein's equations. Constraint equations constitute a necessary condition,as well as sufficient, to consider the spacetime N as the time evolution of a Riemannian hypersurface (m,g) embeded into N with the second fundamental form K. (m,g,K) is then an element of C, the set of initial data solutions to the constraint equations. In this work, we use Robert Bartnik's method to provide a Hilbert submanifold structure on C for weakly asymptotically hyperbolic initial data, whose regularity can be related to the bounded L^{2} curvature conjecture. Difficulties arising from the weakly AH case led us to introduce two second order differential operators and we obtain Poincaré and Korn-type estimates for them. Once the Hilbert structure is properly described, we define a mass functional smooth on the submanifold C and compatible with our weak regularity assumptions. The geometrical invariance of the mass is studied and proven, only up to a weak regularity conjecture about coordinate changes near infinity. Finally, we make a correspondance between critical points of the mass and static metrics
Chaisemartin, Stéphane de. "Modèles eulériens et simulation numérique de la dispersion turbulente de brouillards qui s'évaporent". Thesis, Châtenay-Malabry, Ecole centrale de Paris, 2009. http://www.theses.fr/2009ECAP0011/document.
Texto completo da fonteThe multi-fluid model, providing a Eulerian description of polydisperse sprays, appears as an interesting method for two-phase combustion applications. Its relevance as a numerical tool for industrial device simulations is evaluated in this work. This evaluation assesses the feasibility of multi-fluid simulations in terms of computational cost and analyzes their precision through comparisons with reference methods for spray resolution. In order to define such a reference, the link between the available methods for spray resolution is provided, highlighting their corresponding level of modeling. A first framework of 2-D vortical flows is used to assess the mathematical structure of the multi-fluid model governing system of equations. The link between the mathematical peculiarities and the physical modeling is provided, and a robust numerical scheme efficient for 2-D/3-D configurations is designed. This framework is also used to evaluate the multi-fluid description of evaporating spray sizeconditioned dynamics through quantitative, time-resolved, comparisons with a Lagrangian reference and with experimental data. In order to assess the multi-fluid efficiency in configurations more representative of industrial devices, a numerical solver is designed, providing a framework devoted to spray method evaluation. An original implementation of the multifluid method, combining genericity and efficiency in a parallel framework, is achieved. The coupling with a Eulerian/Lagrangian solver for dispersed two-phase flows, developed at CORIA, is conducted. It allows a precise evaluation of Euler/Lagrange versus Euler/Euler approaches, in terms of precision and computational cost. Finally, the behavior of the multi-fluid model is assessed in 2D-jets and 3-D Homogeneous Isotropic Turbulence. It illustrates the ability of the method to capture evaporating spray dynamics in more complex configurations. The method is shown to describe accurately the fuel vapor mass fraction, a key issue for combustion applications. Furthermore, the method is shown to be efficient in domain decomposition parallel computing framework, a key issue for simulations at the scale of industrial devices
Mazeran, Constant. "Sur la structure mathématique et l'approximation numérique de l'hydrodynamique lagrangienne bidimensionnelle". Bordeaux 1, 2007. http://www.theses.fr/2007BOR13470.
Texto completo da fonteThis work studies a new formulation of compressible Euler equations written in multidimensionnal Lagrangian coordinates, as a system of conservation laws linked to a free divergence constraint; it applies also to an extended physics, including for instance magnetohydrodynamics. This structure allows the mathematical study of the whole Lagrangian problematics, coupling physical unknowns with geometrical one's, associated to the displacement of matter. We prove that the physical part of the system, whose entire formulation is known to be only weakly hyperbolic, is symmetrizable under the differential constraint, although the loss of regularity of geometrical unknowns is characteristic of shear discontinuities. We then derive an original approximate method, of Finite Volumes kind on moving mesh, whose degree of freedom are placed on nodes. The scheme relies only on physical considerations (conservation principle, entropy production), which ensure its stability as well as a result of positivity and non-crossing on triangular mesh. We prove theoretically its convergenge with a rate of on the linearized equations of acoustics. Eventually, we extent the symmeterized structure and numerical method to the case of axisymmetric geometry