Dissertations / Theses on the topic 'L'équation de Boltzmann'
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Xu, Liping. "Contribution à l'étude de l'équation de Boltzmann homogène." Thesis, Paris 6, 2017. http://www.theses.fr/2017PA066018/document.
Full textThis thesis mainly studies the 3D homogeneous Boltzmann equation for hard potentials and moderately soft potentials and the equivalence between some jumping SDE and the corresponding PDE. In particular, we compute the multifractal spectrum of some stochastic processes, study the well-posedness and the propagation of chaos for the Boltzmann equation. The purpose of the first chapter is to study the pathwise properties of the stochastic process $(V_t)_{t\geq0}, representing the time-evolution of the velocity of a typical particle in a gas modeled by the Boltzmann equation for hard or moderately potentials. We show that this process is multifractal and has a deterministic spectrum. For hard potentials, we also give the multifractal spectrum of the process $X_t =\int_0^t V_s ds$, representing the time-evolution of the position of the typical particle. The second chapter is devoted to study the uniqueness of the weak solution to the Boltzmann equation in the class of all measure solutions, in the case of moderately soft potentials. This allows us to obtain a quantitive rate of propagation of chaos for Nanbu particle system for this singular interaction. Finally in the third chapter, we extend Figalli’s work [19] to study the relation between some jumping SDE and the corresponding Fokker-Planck equation. We prove that for any weak solution $(ft)_{t\in[0,T]}$ of the PDE, there exists a weak solution to the SDE of which the time-marginals are given by the family $(f_t)_{t\in[0,T]$
Jrad, Ibrahim. "Analyse spectrale et calcul numérique pour l'équation de Boltzmann." Thesis, Normandie, 2018. http://www.theses.fr/2018NORMR020/document.
Full textIn this thesis, we study the solutions of the Boltzmann equation. We are interested in the homogeneous framework in which the solution f(t; x; v) depends only on the time t and the velocity v. We consider singular crosssections (non cuto_ case) in the Maxwellian case. For the study of the Cauchy problem, we consider a uctuation of the solution around the Maxwellian distribution then a decomposition of this uctuation in the spectral base associated to the quantum harmonic oscillator At first, we solve numerically the solutions using symbolic computation methods and spectral decomposition of Hermite functions. We consider regular initial data and initial conditions of distribution type. Next, we prove that there is no longer a global solution in time for a large initial condition that changes sign (which does not contradict the global existence of a weak solution for a positive initial condition - see for example Villani Arch. Rational Mech. Anal 1998)
Schneider, Jacques. "Une méthode déterministe pour la résolution de l'équation de Boltzmann." Paris 6, 1993. http://www.theses.fr/1993PA066640.
Full textHammouch, Jillal. "Limite hydrodynamique des modèles discrets et semidiscrets de l'équation de Boltzmann." Paris 7, 1995. http://www.theses.fr/1995PA077035.
Full textHamzeh, Hani. "Résolution de l'équation de transport de Boltzmann pour les phonons et applications." Phd thesis, Université Paris Sud - Paris XI, 2012. http://tel.archives-ouvertes.fr/tel-00778705.
Full textMieussens, Luc. "Modèles à vitesses discrètes et méthodes numériques pour l'équation de Boltzmann-BGK." Bordeaux 1, 1999. http://www.theses.fr/1999BOR10605.
Full textDolmaire, Théophile. "Etude mathématique de la dérivation de l'équation de Boltzmann dans un domaine à bord." Thesis, Université de Paris (2019-....), 2019. http://www.theses.fr/2019UNIP7108.
Full textThe Boltzmann equation is a model introduced in order to describe diluted gases. The solutions of this equation present an interesting behaviour: they converge irreversibly towards a determined equilibrium. However, the Boltzmann equation is formally obtained using a microscopic description of the matter, in which the interactions between the atoms constituting the gas are time-reversible. From this paradox has emerged the question of a mathematically rigorous derivation of the Boltzmann equation.In this work one has obtained such a derivation in the case of a domain with a boundary (Lanford obtained this derivation in the case when the domain is the whole Euclidean space, which was historically speaking the first rigorous derivation of the Boltzmann equation), by prescribing the specular reflexion as the way the particles and the boundary of the domain interact. The domain here will be the half-space.This derivation is using sequences of equations, namely the BBGKY and the Boltzmann hierarchies. After a presentation of the formal derivation of those hierarchies in the case of a domain with boundary, one has carefully addressed the rigorous definition of those hierarchies, detailing the appropriate functional setting. In a second part, the proof of the convergence of the solutions of the BBGKY hierarchy towards the solutions of the Boltzmann hierarchy is presented exhaustively. In particular, the geometrical control of the recollisions in the case of the half-space has been written in the most comprehensive way
Hamdache, Kamal Ahmed. "Sur l'existence globale et le comportement asymptotique de quelques solutions de l'équation de Boltzmann." Paris 6, 1986. http://www.theses.fr/1986PA066225.
Full textGoudon, Thierry. "Sur quelques questions relatives à la théorie cinétique des gaz et à l'équation de Boltzmann." Bordeaux 1, 1997. http://www.theses.fr/1997BOR10508.
Full textGUERIN, Hélène. "Interprétation probabiliste de l'équation de Landau." Phd thesis, Université de Nanterre - Paris X, 2002. http://tel.archives-ouvertes.fr/tel-00002066.
Full textMao, Lili. "Contribution à la résolution de l'équation de Boltzmann en multigroupe par les méthodes déterministes et Monte Carlo." Aix-Marseille 1, 1998. http://www.theses.fr/1998AIX11026.
Full textSirbu, Marina. "Couplage des équations de Maxwell avec l'équation de Boltzmann en 3D : appliqué à la modélisation d'un photocommutateur THz." Paris 11, 2005. http://www.theses.fr/2005PA112255.
Full textThis PhD thesis presents the coupling between the Boltzmann transport equations and the electromagnetic field equations in a photoconductive switch generating THz signals. First, the transport equations are solved in the drift diffusion approximation. Then, a more complex resolution is made with a Monte Carlo based model. The photoconductive switch is located is coplanar wave guide whose dimensions are comparables with the existents structures. The numerical constraints come from the time dependant resolution, the necessarily space mesh, the simulation domain dimensions, boundary conditions and non linearity introduced by the time and space coefficients variation. The 3D equation system is solved with the variable space step FDTD (Finite Difference Time Domain) method, which allows a sufficiently refined mesh inside the switch. We have studied the photoconductive switch response when a femto second optic excitation is applied. We have shown the electromagnetic field implication in the device response origin. We also made a parametric analysis identifying the main parameters controlling the electromagnetic THz pulse. There is a good agreement between the modelling results and the experimental data. The Monte Carlo method allows taking into account the inertial effects between the electromagnetic field variation and the carrier response. This method is still in developing phase, but we have obtained good preliminary results
Piaud, Benjamin. "Modélisation mésoscopique des écoulements avec changement de phase à partir de l'équation de Boltzmann-Enskog : introduction des effets thermiques." Phd thesis, Toulouse 3, 2007. http://tel.archives-ouvertes.fr/tel-00931543.
Full textTabikh, Sleiman. "Méthodes rapides de résolution de l'équation de Boltzmann en régime de porteurs chauds par développement sur des fonctions de base." Montpellier 2, 1987. http://www.theses.fr/1987MON20121.
Full textNtovoris, Eleftherios. "Contribution à la théorie des EDP non linéaires avec applications à la méthode des surfaces de niveau, aux fluides non newtoniens et à l'équation de Boltzmann." Thesis, Paris Est, 2016. http://www.theses.fr/2016PESC1057/document.
Full textThis thesis consists of three different and independent chapters, concerning the mathematical study of three distinctive physical problems, which are modelled by three non- linear partial differential equations. These equations concern the level set method, the theory of incompressible flow of non-Newtonian materials and the kinetic theory of rare- fied gases. The first chapter of the thesis concerns the dynamics of moving interfaces and contains a rigorous justification of a numerical procedure called re-initialization, for which there are several applications in the context of the level set method. We apply these results for first order level set equations. We write the re-initialization procedure as a splitting algorithm and study the convergence of the algorithm using homogenization techniques in the time variable. As a result of the rigorous analysis, we are also able to introduce a new method for the approximation of the distance function in the context of the level set method. In the case where one only looks for a level set function with gradient bounded from below near the zero level, we propose a simpler approximation. In the general case where the zero level might present changes of topology we introduce a new notion of relaxed limits. In the second chapter of the thesis, we study a free boundary problem arising in the study of the flow of an incompressible non-Newtonian material with Drucker-Prager plasticity on an inclined plane. We derive a subdifferential equation, which we reformulate as a variational problem containing a term with linear growth in the gradient variable, and we study the problem in an unbounded domain. We show that the equations are well posed and satisfy some regularity properties. We are then able to connect the physical parameters with the abstract problem and prove some quantitative properties of the solution. In particular, we show that the solution has compact support and the support is the free boundary. We also construct explicit solutions of an ordinary differential equation, which we use to estimate the free boundary. The last chapter of the thesis is dedicated to the study of infinite energy solutions of the homogeneous Boltzmann equation with Maxwellian molecules. We obtain new results concerning the existence of eternal solutions in the space of probability measure with infinite energy (i.e. the second order moment is infinite). These solutions describe the asymptotic behaviour of other infinite energy solutions but could also be useful in the study of intermediate asymptotic states of solutions with finite but arbitrarily large energy. We use harmonic analysis tools to study the equation, where the velocity variable is expressed in the Fourier space. Finally, a logarithmic scaling of the time variable allows to determine the correct asymptotic scaling of the solutions