Dissertations / Theses on the topic 'Dérivée fractionnaire'
Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles
Consult the top 34 dissertations / theses for your research on the topic 'Dérivée fractionnaire.'
Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.
You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.
Browse dissertations / theses on a wide variety of disciplines and organise your bibliography correctly.
Drouilhet, Rémy. "Dérivée de mouvement brownien fractionnaire et estimation de densité spectrale." Pau, 1993. http://www.theses.fr/1993PAUU3024.
Full textBorla, Andreea. "Estimation non paramétrique de la dérivée fractionnaire de la fonction de répartition : avec une application statistique aux tests d'ajustement." Aix-Marseille 2, 2010. http://www.theses.fr/2010AIX24005.
Full textWe propose an estimator for the (a) fractional derivative of a distribution function. The estimator is based on finite differences of the empirical distribution function. The asymptotic bias, variance and consistency of the estimator are studied. It depends on a "smoothing parameter" whose behavior is similar to the bandwidth of a kernel estimator. Given that we note that an endogenous truncation can be defined in a natural way, we discuss the implementation of a truncated version of the estimator. This will allow a sharper analysis of the asymptotic behaviour of the estimator with respect to the sample size and the order of the fractional derivative. In the third chapter we will introduce another estimator for the CDF, a smoother one, the kernel estimator, and thus a second smothing factor. A natural endogenous truncation to the right ensures a tractacle definition in practice and allows deducing the asymptotic properties of the estimator. The optimal choice of the smoothing parameters is studied. Finally, we propose a goodness-of-fit test. Using simulations, we will show that there is an optimal order of differentiation that maximizes the power of the test, which depends on the alternative. Consequently test based on the integer order derivatives are not necessarily the one with the highest power. The optimum order of differentiation changes depending on the parameters of the alternative distribution and the sample size
Hnaien, Dorsaf. "Equations aux dérivées fractionnaires : propriétés et applications." Thesis, La Rochelle, 2015. http://www.theses.fr/2015LAROS038.
Full textOur objective in this thesis is the study of nonlinear differential equations involving fractional derivatives in time and/or in space. First, we are interested in the study of two nonlinear time and/or space fractional systems. Our second interest is devoted to the analysis of a time fractional differential equation. More exactly for the first part, the question concerning the global existence and the asymptotic behavior of a nonlinear system of differential equations involving time and space fractional derivatives is addressed. The used techniques rest on estimates obtained for the fundamental solutions and the comparison of some fractional inequalities. In addition, we study a nonlinear system of reaction-diffusion equations with space fractional derivatives. The local existence and the uniqueness of the solutions are proved using the Banach fixed point theorem. We show that the solutions are bounded and analyze their large time behavior. The second part is dedicated to the study of a nonlinear time fractional differential equation. Under some conditions on the initial data, we show that the solution is global while under others, it blows-up in a finite time. In this case, we give its profile as well as bilateral estimates of the blow-up time. While for the global solution we study its asymptotic behavior
Hadouni, Doha. "Détection de rupture hors ligne sur des processus dépendants." Thesis, Université Clermont Auvergne (2017-2020), 2017. http://www.theses.fr/2017CLFAC098.
Full textJoseph, Claire. "Sur le contrôle optimal des équations de diffusion et onde fractionnaires en temps à données incomplètes." Thesis, Antilles, 2017. http://www.theses.fr/2017ANTI0164/document.
Full textIn this thesis, we are interested in the résolution of optimal control problems associated to fractional diffusion-wave equations in time with incomplete data, and where derivatives are understood in Riemann-Liouville sense
Lassoued, Rafika. "Contributions aux équations d'évolution frac-différentielles." Thesis, La Rochelle, 2016. http://www.theses.fr/2016LAROS001/document.
Full textIn this thesis, we are interested in fractional differential equations. We begin by studying a time fractional differential equation. Then we study three fractional nonlinear systems ; the first system contains a fractional Laplacian, while the others contain a time fractional derivative in the sense of Caputo. In the second chapter, we establish the qualitative properties of the solution of a time fractional equation which describes the evolution of certain species. The existence and uniqueness of the global solution are proved for certain values of the initial condition. In this case, the asymptotic behavior of the solution is dominated by t^α. Under another condition, the solution blows-up in a finite time. The solution profile and the blow-up time estimate are established and a numerical confirmation of these results is presented. The chapters 4, 5 and 6 are dedicated to the study of three fractional systems : an anomalous diffusion system which describes the propagation of an infectious disease in a confined population with a SIR type, the time fractional Brusselator and a time fractional reaction-diffusion system with a balance law. The study includes the global existence and the asymptotic behavior. The existence and uniqueness of the local solution for the three systems are obtained by the Banach fixed point theorem. However, the asymptotic behavior is investigated by different techniques. For the first system our results are proved using semi-group estimates and the Sobolev embedding theorem. Concerned the time fractional Brusselator, the used technique is based on an argument of feedback. Finally, a maximal regularity result is used for the last system
Vigué, Pierre. "Solutions périodiques et quasi-périodiques de systèmes dynamiques d'ordre entier ou fractionnaire : applications à la corde frottée." Thesis, Aix-Marseille, 2017. http://www.theses.fr/2017AIXM0306/document.
Full textThe continuation of periodic and quasi-periodic solutions is performed on several models derived from the violin. The continuation for a one degree-of-freedom model with a regularized friction shows, compared with Coulomb friction, the persistence of limit cycle bifurcations (a maximum bow speed and a minimum normal force allowing Helmholtz motion) and of global properties of the solution branch (increase of amplitude with respect to the bow speed, decrease of frequency with respect to the normal force). The Harmonic Balance Method is assessed on this regularized friction system and shows interesting convergence properties (the error is low, monotone and rapidly decreasing). For two modes the continuation shows higher register solutions with a plausible stability. A stronger inharmonicity can greatly modify the bifurcation diagram. A new method is proposed for the continuation of quasi-periodic solutions. It couples a two-pulsations HBM with the Asymptotic Numerical Method. We have taken great care to deal efficiently with large systems of unknowns. A model of friction that takes into account temperature of the contact zone is reformulated with a fractional derivative. We then propose a method of continuation of periodic solutions for differential systems that contain fractional operators. Their definition is usually restricted to causal solutions, which prevents the existence of periodic solutions. Having chosen a specific definition of fractional operators to avoid this issue we establish a sufficient condition on asymptotically attractive cycles in the causal framework to be solutions of our framework
Akil, Mohammad. "Quelques problèmes de stabilisation directe et indirecte d’équations d’ondes par des contrôles de type fractionnaire frontière ou de type Kelvin-Voight localisé." Thesis, Limoges, 2017. http://www.theses.fr/2017LIMO0043/document.
Full textThis thesis is devoted to study the stabilization of the system of waves equations with one boundary fractional damping acting on apart of the boundary of the domain and the stabilization of a system of waves equations with locally viscoelastic damping of Kelvin-Voight type. First, we study the stability of the multidimensional wave equation with boundary fractional damping acting on a part of the boundary of the domain. Second, we study the stability of the system of coupled onedimensional wave equation with one fractional damping acting on a part of the boundary of the domain. Next, we study the stability of the system of coupled multi-dimensional wave equation with one fractional damping acting on a part of the boundary of the domain. Finally, we study the stability of the multidimensional waves equations with locally viscoelastic damping of Kelvin-Voight is applied for one equation around the boundary of the domain
Ossman, Hala. "Etude mathématique de la convergence de la PGD variationnelle dans certains espaces fonctionnels." Thesis, La Rochelle, 2017. http://www.theses.fr/2017LAROS006/document.
Full textIn this thesis, we are interested in the PGD (Proper Generalized Decomposition), one of the reduced order models which consists in searching, a priori, the solution of a partial differential equation in a separated form. This work is composed of five chapters in which we aim to extend the PGD to the fractional spaces and the spaces of functions of bounded variation and to give theoretical interpretations of this method for a class of elliptic and parabolic problems. In the first chapter, we give a brief review of the litterature and then we introduce the mathematical notions and tools used in this work. In the second chapter, the convergence of rank-one alternating minimisation AM algorithms for a class of variational linear elliptic equations is studied. We show that rank-one AM sequences are in general bounded in the ambient Hilbert space and are compact if a uniform non-orthogonality condition between iterates and the reaction term is fulfilled. In particular, if a rank-one (AM) sequence is weakly convergent then it converges strongly and the common limit is a solution of the alternating minimization problem. In the third chapter, we introduce the notion of fractional derivatives in the sense of Riemann-Liouville and then we consider a variational problem which is a generalization of fractional order of the Poisson equation. Basing on the quadratic nature and the decomposability of the associated energy, we prove that the progressive PGD sequence converges strongly towards the weak solution of this problem. In the fourth chapter, we benefit from tensorial structure of the spaces BV with respect to the weak-star topology to define the PGD sequences in this type of spaces. The convergence of this sequence remains an open question. The last chapter is devoted to the d-dimensional heat equation, we discretize in time and then at each time step one seeks the solution of the elliptic equation using the PGD. Then, we show that the piecewise linear function in time obtained from the solutions constructed using the PGD converges to the weak solution of the equation
Inizan, Pierre. "Dynamique fractionnaire pour le chaos hamiltonien." Observatoire de Paris (1667-....), 2010. https://theses.hal.science/tel-01958537.
Full textMany properties of chaotic Hamiltonian systems have been exhibited by numerical simulations but still remain not properly understood. Among various directions of research, Zaslavsky carries on an analysis which involves fractional derivatives. Even if his work is not fully formalized, his results seem promising. Fractional calculus, also used in several other fields, generalizes differential equations in order to take into account some complex phenomena. Concerning Lagrangian and Hamiltonian systems, the fractional embedding developped by Cresson provides a procedure based on the least action principle to build fractional dynamical equations. The main goal of the thesis consists in using this formalism to consolidate Zaslavsky's work. After a presentation of the fractional calculus adapted to our work, we enhance the fractional embedding by reconciling it with the causality principle and by making it dimensionally homogeneous. Once this formal framework is established we try to understand how a fractional dynamics can emerge in chaotic Hamiltonian systems, through two tracks respectively based on Stanislavsky's and Hilfer's works. The first one faces two difficulties, but the second leads to a simple dynamical model, where a fractional derivative appears when Zaslavsky's analysis is taken into account. We finally leave chaotic systems to show that thanks to the causal formulation of the fractional embedding, some classical dissipative equations reveal fractional Lagrangian structures, which could be of numerical interest
Malik, Salman Amin. "Contributions aux équations aux dérivées fractionnaires et au traitement d'images." Phd thesis, Université de La Rochelle, 2012. http://tel.archives-ouvertes.fr/tel-00825874.
Full textDebbi, Latifa. "Equations aux dérivées partielles déterministes et stochastiques avec opérateurs fractionnaires." Nancy 1, 2006. http://www.theses.fr/2006NAN10046.
Full textThis 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
Nourdin, Ivan. "Contributions à l'étude des processus gaussiens." Habilitation à diriger des recherches, Université Pierre et Marie Curie - Paris VI, 2008. http://tel.archives-ouvertes.fr/tel-00287738.
Full textLe chapitre 2 présente des théorèmes limites abstraits (principalement valables pour une suite (F_n) d'intégrales multiples par rapport à un processus gaussien isonormal X) sous des hypothèses concernant la dérivée de Malliavin de F_n. Nous y exposons notamment une nouvelle méthode donnant (de manière étonnament simple) une estimation de type Berry-Esséen quand la suite (F_n) converge en loi vers une gaussienne. En particulier, cette méthode permet d'estimer la vitesse de convergence dans le classique théorème de Breuer et Major. Notons que les outils présentés dans ce chapitre sont la base des résultats obtenus dans le premier chapitre.
Le chapitre 3 est consacré à mes travaux relatifs à la théorie de l'intégration contre des ``chemins rugueux'' (rough paths en anglais). Tout d'abord, nous faisons un lien avec l'intégration par régularisation à la Russo-Vallois. Ensuite, nous étudions un problème de contrôle optimal. Enfin, nous exploitons l'intégration algébrique récemment introduite par Gubinelli pour calculer le développement asymptotique de la ``loi'' de la solution d'une équation différentielle stochastique dirigée par un brownien fractionnaire d'une part, et pour étudier les équations différentielles avec retard dirigées par un chemin rugueux d'autre part.
Enfin, dans le chapitre 4, nous définissons et étudions un nouvel objet, appelé ``dérivée stochastique''. Puis, nous illustrons certains phénomènes généraux en appliquant cette théorie au cas du mouvement brownien fractionnaire avec dérive.
Rakotonasy, Solonjaka Hiarintsoa. "Modèle fractionnaire pour la sous-diffusion : version stochastique et edp." Phd thesis, Université d'Avignon, 2012. http://tel.archives-ouvertes.fr/tel-00839892.
Full textOuloin, Martyrs. "Méthode d'inversion d'un Modèle de diffusion Mobile Immobile fractionnaire." Phd thesis, Université d'Avignon, 2012. http://tel.archives-ouvertes.fr/tel-01016447.
Full textOuloin, Martyrs. "Méthode d’inversion d’un Modèle de diffusion Mobile Immobile fractionnaire." Thesis, Avignon, 2012. http://www.theses.fr/2012AVIG0504/document.
Full textAppealing models for mass transport in porous media assume that fluid and tracer particles can be trapped during random periods. Among them, the fractional version of the Mobile Immobile Model (f-MIM) was found to agree with several tracer test data recorded in environmental media.This model is equivalent to a stochastic process whose density probability function satisfies an advection-diffusion equation equipped with a supplementary time derivative, of non-integer order. The stochastic process is the hydrodynamic limit of random walks accumulating convective displacements, diffusive displacements, and stagnation steps of random duration distributed by a stable Lévy law having no finite average. Random walk and fractional differential equation provide complementary simulation methods.We describe that methods, in view of having tools for comparing the model with tracer test data consisting of time concentration curves. An other essential step in this direction is finding the four parameters of the fractional equation which make its solutions fit at best given sets of such data. Hence, we also present an inversion method adapted to the f-MIM. This method is based on Laplace transform. It exploits the link between model's parameters and Laplace transformed solutions to f-MIM equation. The link is exact in semi-infinite domains. After having checked inverse method's efficiency for numerical artificial data, we apply it to real tracer test data recorded in non-saturated porous sand
Bourdet, Ana Cristina. "Atténuation des réponses transitoires par traitement hybride piézoélectrique / viscoélastique en utilisant un modèle à dérivées fractionnaires." Paris, CNAM, 2004. http://www.theses.fr/2004CNAM0482.
Full textThis work presents a finite element formulation for vibration reduction of an adaptive sandwich beam composed of a viscoelastic core and elastic/piezoelectric laminated faces. The electromechanical coupling is taken into account by modifying the stiffness matrix of the piezoelectric layers (sensor) and by applying a mechanical load written in terms of the applied tension (actuator). The finite element formulation has no electrical degrees-of-freedom. The fractional derivative Zener model is used to characterize the viscoelastic behaviour of the core. Equations of motion are solved using a direct time integration method based on the Newmark scheme in conjunction with the Grünwald approximation of fractional derivatives. An extension to finite displacements and rotations into the finite element formulation is proposed
Denis, Yvan. "Modélisation en grandes déformations du comportement hystérétique des renforts de composites : Application à l'estampage incrémental." Thesis, Lyon, 2019. http://www.theses.fr/2019LYSEI098.
Full textComposite materials are experiencing exponential growth in use in the aerospace, aeronautics, automotive and sports sectors. This significant development is mainly due to the excellent mechanical properties offered by this type of material. In addition, the ratio characteristics/weight is extremely advantageous since they remain lighter than the materials usually used in the past. However, they are also extremely expensive and moderately understood compared to the scientific knowledge that exists for crystalline materials. Numerical simulation tool has therefore become an integral part of the improvement of shaping processes, which requires the development of mechanical models. Until now, given stamping strategies using a single punch/matrix pair, the loads were assumed to be monotonous and therefore the associated behavioural laws were hyperelastic or viscoelastic. However, given that industrial demand is constantly growing and the complexity of the geometries which is also increasing, we propose, through the work presented here, innovative and original approaches such as incremental forming and the management of boundary conditions. These new approaches induce cyclic loading variations in shear or bending and hyperelastic models are therefore no longer enough reliable to properly model stamping processes. As the study of hysteresis behaviour is new for composite materials, the work presented then focuses on dry reinforcements. Thus, an experimental approach was carried out to determine the reaction of the fabric once it was subjected to cyclic loading. Then, dissipative hysteretic models were established for integration into finite element calculation software. Finally, numerical simulations with experimental comparisons are proposed, initially basic to validate the model and then more complex to show the interest of such models and strategies
Delmas, Bruno. "Comment améliorer la dérive des résonateurs à quartz pour applications spatiales ?" Phd thesis, Université de Franche-Comté, 2009. http://tel.archives-ouvertes.fr/tel-00536860.
Full textFarah, Mohamed. "Estimation paramétrique de systèmes gouvernés par des équations aux dérivées partielles." Thesis, Poitiers, 2016. http://www.theses.fr/2016POIT2311.
Full textIn this manuscript, a special attention is paid to the identification of dynamic systems whose behavior is governed by partial differential equations (PDE). To achieve this, two identification algorithms are proposed. The first is an equation-error algorithm based on reinitialized partial moments whose function is to make the terms of partial derivatives disappear. The parameters of the resulting model can then be estimated by a least squares type approach. This method requires the selection of a synthesis parameter and a large number of sensors distributed over the entire geometry of the studied system. A study of the optimal choice of the synthesis parameters as well as of the influence of the number and distribution of the sensors is conducted on a numerical example. The second algorithm is associated to the PDE that can be presented by a Roesser model. Throughout this model, a fractional linear formulation is proposed and an output-error algorithm is exploited to estimate the model parameters. The initialization of this algorithm is achieved thanks to the results provided by the first algorithm. Finally, the efficiency of the two proposed approaches is shown through a numerical example of a co-current heat exchanger
Fellah, Zine El Abiddine. "Propagation acoustique dans les milieux poreux hétérogènes." Habilitation à diriger des recherches, Université de la Méditerranée - Aix-Marseille II, 2007. http://tel.archives-ouvertes.fr/tel-00477405.
Full textTouibi, Rim. "Sur le comportement qualitatif des solutions de certaines équations aux dérivées partielles stochastiques de type parabolique." Thesis, Université de Lorraine, 2018. http://www.theses.fr/2018LORR0263/document.
Full textThis thesis is concerned with stochastic partial differential equations of parabolic type. In the first part we prove new results regarding the existence and the uniqueness of global and local variational solutions to a Neumann initial-boundary value problem for a class of non-autonomous stochastic parabolic partial differential equations. The equations we consider are defined on unbounded open domains in Euclidean space satisfying certain geometric conditions, and are driven by a multiplicative noise derived from an infinite-dimensional fractional Wiener process characterized by a sequence of Hurst parameters H = (Hi) i ∈ N+ ⊂ (1/2,1). These parameters are in fact subject to further constraints that are intimately tied up with the nature of the nonlinearity in the stochastic term of the equations, and with the choice of the functional spaces in which the problem at hand is well-posed. Our method of proof rests on compactness arguments in an essential way. The second part is devoted to the study of the blowup behavior of solutions to semilinear stochastic partial differential equations with Dirichlet boundary conditions driven by a class of differential operators including (not necessarily symmetric) Lévy processes and diffusion processes, and perturbed by a mixture of Brownian and fractional Brownian motions. Our aim is to understand the influence of the stochastic part and that of the differential operator on the blowup behavior of the solutions. In particular we derive explicit expressions for an upper and a lower bound of the blowup time of the solution and provide a sufficient condition for the existence of global positive solutions. Furthermore, we give estimates of the probability of finite time blowup and for the tail probabilities of an upper bound for the blowup time of the solutions
Lafleche, Laurent. "Dynamique de systèmes à grand nombre de particules et systèmes dynamiques." Thesis, Paris Sciences et Lettres (ComUE), 2019. http://www.theses.fr/2019PSLED010.
Full textIn this thesis, we study the behavior of solutions of partial differential equations that arise from the modeling of systems with a large number of particles. The dynamic of all these systems is driven by interaction between the particles and external and internal forces. However, we will consider different scales and travel from the quantum level of atoms to the macroscopic level of stars. We will see that differences emerge from the associated dynamics even though the main properties are conserved. In this journey, we will cross the path of various applications of these equations such as astrophysics, plasma, semi-conductors, biology, economy. This work is divided in three parts.In the first one, we study the semi classical behavior of the quantum Hartree equation and its limit to the kinetic Vlasov equation. Properties such as the propagation of moments and weighted Lebesgue norms and dispersive estimates are quantified uniformly in the Planck constant and used to establish stability estimates in a semiclassical analogue of the Wasserstein distance between the solutions of these two equations.In the second part, we investigate the long time behavior of macroscopic and kinetic models where the collision operatoris linear and has a heavy-tailed local equilibrium, such as the Fokker-Planck operator, the fractional Laplacian with a driftor a Linear Boltzmann operator. This let appear two main techniques, the entropy method and the positivity method.In the third part, we are interested in macroscopic models inspired from the Keller-Segel equation, and we study therange of parameters under which the system collapses, disperses or stabilizes. The first effect is studied using appropriate weights, the second using Wasserstein distances and the third using Lebesgue norms
Abdelkaled, Houda. "Caractère bien posé probabiliste pour une équation non linéaire faiblement dispersive." Thesis, CY Cergy Paris Université, 2020. http://www.theses.fr/2020CYUN1075.
Full textWe propose in this thesis to study the propagation of non-linear wavesin the high frequency regime by methods from probability theoryand the theory of partial differential equations. We consider the cubic fractional wave equation, posed on a bounded domain of Euclidean space, with conditionsat the edge periodic. We will show to begin with, on which spaces this problem iswell-posed in Hadamard’s sense using fixed point methods. Then, we're going to proof high frequency instability results that shows thelimit of standard methods. Finally, we will consider building probabilistic measures on the space of the initial data such as in the context of the instability results, a well-posedness form persists, almost surely
Faria, Albert Willian. "Modelagem por elementos finitos de placas compostas: contribuição ào estudo do amortecimento, dano e incertezas." Universidade Federal de Uberlândia, 2010. https://repositorio.ufu.br/handle/123456789/14696.
Full textDoutor em Engenharia Mecânica
No estado tecnológico atual, os materiais compostos são cada vez mais utilizados em produtos de alta tecnologia, sobretudo no setor aeroespacial, em virtude de sua resistência/peso superior às dos materiais metálicos, e em virtude de sua elevada rigidez e resistência mecânica à fadiga. Além disso, devido ao seu melhor comportamento ao choque mecânico e à combustão química, as estruturas em material composto oferecem uma boa condição de segurança. Estruturas fabricadas em material composto ou metálico são submetidas a uma grande variedade de carregamentos mecânicos ao longo de sua vida útil, que podem ser dependentes ou independentes do tempo, quer dizer, de natureza estática ou dinâmica. Acima das condições de serviço para as quais elas são concebidas, no domínio estático ou dinâmico, as estruturas compostas podem desenvolver diferentes formas de dano em seus elementos constitutivos. Nas ultimas décadas, devido a sua capacidade de absorver e dissipar sob a forma de calor uma parte da energia de vibração dos sistemas estruturais, os materiais viscoelásticos vêm sendo intensamente empregados para reduzir os níveis de vibração e sonoros indesejáveis no domínio da dinâmica das estruturas. Nesta tese, estes materiais são aplicados sob a forma de tratamento interno em estruturas compostas, que permite o aumento das deformações por cisalhamento da camada viscoelástica e, assim, a dissipação da energia de vibração e a diminuição do dano. Interessa-se também, neste trabalho, o estudo de um mecanismo interno de dano ao nível da matriz polimérica no domínio dinâmico. Este mecanismo de dano é muito comum nos materiais estratificados constituídos de fibras orientadas em uma única direção. Nesta tese, é apresentada a modelagem por elementos finitos utilizando os elementos retangulares Serendipity, a oito pontos nodais, de placa composta, considerando três diferentes teorias para a aproximação do campo de deslocamento mecânico: FSDT (First-order Shear Deformation Theory), HSDT (Higher-order Shear Deformation Theory) e Layerwise-FSDT. As duas primeiras teorias permitem a modelagem de estruturas com multicamadas e a segunda é formulada para uma configuração assimétrica formada por três camadas, cuja formulação é obtida pela imposição da continuidade dos deslocamentos ao longo da espessura do estratificado. Estas teorias são implementadas em ambiente MATLAB® para a modelagem de modelos EF de estruturas compostas de geometria simples. Para considerar a dependência no domínio da freqüência e do tempo das propriedades dos materiais viscoelásticos, a aproximação através do uso do Modulo Complexo é utilizada. No entanto, para levar em conta sua dependência no domínio do tempo e da temperatura utiliza-se a aproximação através do uso de Derivadas Fracionárias. Utiliza-se também, neste trabalho, o emprego do Modelo Histerético Complexo (independente do tempo, da temperatura e da freqüência) para considerar o amortecimento natural das camadas do estratificado. Além disso, esta tese propõe o uso de uma metodologia de propagação de incertezas em estruturas compostas. Para isso, adota-se a aproximação de Karhunen-Loève para a discretização do campo aleatório bidimensional. E, através de diversas simulações numéricas, são ilustrados os temas abordados ao longo deste trabalho de tese.
Blanc, Emilie. "Time-domain numerical modeling of poroelastic waves : the Biot-JKD model with fractional derivatives." Phd thesis, Aix-Marseille Université, 2013. http://tel.archives-ouvertes.fr/tel-00954506.
Full textAssaf, Riad. "Modélisation des phénomènes de diffusion thermique dans un milieu fini homogène en vue de l’analyse, de la synthèse et de la validation de commandes robustes." Thesis, Bordeaux, 2015. http://www.theses.fr/2015BORD0271/document.
Full textThe work of this thesis concerns the study of the thermal diffusion phenomena to have a model (white box approach) for the analysis, the frequency synthesis and the time validation of robust commands. The Part 1 composed of chapter 1 focuses on the definitions and the interpretations of the integro-differential non-integer operator. The simulation problem in the time domain of the fractional differential systems is specified. Part 2 entitled "Analytical Study" includes two chapters whose objective is to make a detailed analysis of the fractional order behavior, first in a semi-infinite medium (chapter 2), then in a finite medium (chapter 3). Part 3, entitled "Numerical simulation of time responses" combining two chapters (4 and 5), aims the implementation of the "thermal process" plant (model validation of a finite medium) of a simulator of the thermal control loop time responses
Fernández, Sánchez Antonio J. "Existence et multiplicité de solutions pour des problèmes elliptiques avec croissance critique dans le gradient." Thesis, Valenciennes, 2019. http://www.theses.fr/2019VALE0020/document.
Full textIn this thesis, we provide existence, non-existence, uniqueness and multiplicity results for partial differential equations with critical growth in the gradient. The principal techniques employed in our proofs are variational techniques, lower and upper solution theory, a priori estimates and bifurcation theory. The thesis consists of six chapters. In chapter 0, we introduce the topic of the thesis and we present the main results. Chapter 1 deals with a p-Laplacian type equation with critical growth in the gradient. This equation will depend on a real parameter. Depending on the interval where this parameter lives, we obtain the existence and uniqueness of one solution or we prove the existence and multiplicity of solutions. In chapters 2 and 3, we continue our study in the case where the operator is the Laplacian. However, unlike chapter 1, we study the case where the coefficient functions may change sign. We obtain again existence and multiplicity results. In chapter 4, we study non-local problems of fractional Laplacian type with different non-local gradient terms. We prove existence and non-existence results for different equations of this type. Finally, in chapter 5, we present some open problems related to the content of the thesis and some research perspectives
Dannawi, Ihab. "Contributions aux équations d'évolutions non locales en espace-temps." Thesis, La Rochelle, 2015. http://www.theses.fr/2015LAROS007/document.
Full textIn this thesis, we study four non-local evolution equations. The solutions of these four equations can blow up in finite time. In the theory of nonlinear evolution equations, a solution is qualified as global if it isdefined for any time. Otherwise, if a solution exists only on a bounded interval [0; T), it is called local solution. In this case and when the maximum time of existence is related to a blow up alternative, we say that the solution blows up in finite time. First, we consider the nonlinear Schröodinger equation with a fractional power of the Laplacien operator, and we get a blow up result in finite time Tmax > 0 for any non-trivial non-negative initial condition in the case of sub-critical exponent. Next, we study a damped wave equation with a space-time potential and a non-local in time non-linear term. We obtain a result of local existence of a solution in the energy space under some restrictions on the initial data, the dimension of the space and the growth of nonlinear term. Additionally, we get a blow up result of the solution in finite time for any initial condition positive on average. In addition, we study a Cauchy problem for the evolution p-Laplacien equation with nonlinear memory. We study the local existence of a solution of this equation as well as a result of non-existence of global solution. Finally, we study the maximum interval of existence of solutions of the porous medium equation with a nonlinear non-local in time term
Vilmart, Gilles. "Étude d'intégrateurs géométriques pour des équations différentielles." Phd thesis, Université Rennes 1, 2008. http://tel.archives-ouvertes.fr/tel-00348112.
Full textDans 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.
Mignot, Rémi. "Réalisation en guides d'ondes numériques stables d'un modèle acoustique réaliste pour la simulation en temps-réel d'instruments à vent." Phd thesis, Télécom ParisTech, 2009. http://tel.archives-ouvertes.fr/tel-00456997.
Full textGuelmame, Billel. "Sur une régularisation hamiltonienne et la régularité des solutions entropiques de certaines équations hyperboliques non linéaires." Thesis, Université Côte d'Azur, 2020. https://tel.archives-ouvertes.fr/tel-03177654.
Full textIn this thesis, we study some non-dispersive conservative regularisations for the scalar conservation laws and also for the barotropic Euler system. Those regularisations are obtained inspired by a regularised Saint-Venant system introduced by Clamond and Dutykh in 2017. We also study the regularity, in generalised BV spaces, of the entropy solutions of some nonlinear hyperbolic equations. In the first part, we obtain and study a suitable regularisation of the inviscid Burgers equation, as well as its generalisation to scalar conservation laws. We prove that this regularisation is locally well-posedness for smooth solutions. We also prove the global existence of solutions that satisfy a one-sided Oleinik inequality for uniformly convex fluxes. When the regularising parameter ``l’’ goes to zero, we prove that the solutions converge, up to a subsequence, to the solutions of the original scalar conservation law, at least for a short time. We also generalise the regularised Saint-Venant equations to obtain a regularisation of the barotropic Euler system, and the Saint-Venant system with uneven bottom. We prove that both systems are locally well-posed in Hs, with s ≥ 2. In the second part, we prove a regularising effect, on the initial data, of scalar conservation laws with Lipschitz strictly convex flux, and of scalar equations with a linear source term. For some cases, we give a limit of the regularising effect.Finally, we prove the global existence of entropy solutions of a class of triangular systems involving a transport equation in BV^s x L^∞ where s > 1/3
Tristani, Isabelle. "Existence et stabilité de solutions fortes en théorie cinétique des gaz." Thesis, Paris 9, 2015. http://www.theses.fr/2015PA090013/document.
Full textThe topic of this thesis is the study of models coming from kinetic theory. In all the problems that are addressed, the associated linear or linearized problem is analyzed from a spectral point of view and from the point of view of semigroups. Tothat, we add the study of the nonlinear stability when the equation is nonlinear. More precisely, to begin with, we treat the problem of trend to equilibrium for the fractional Fokker-Planck and Boltzmann without cut-off equations, proving an exponential decay to equilibrium in spaces of type L1 with polynomial weights. Concerning the inhomogeneous Landau equation, we develop a Cauchy theory of perturbative solutions in spaces of type L2 with various weights such as polynomial and exponential weights and we also prove the exponential stability of these solutions. Then, we prove similar results for the inhomogeneous inelastic diffusively driven Boltzmann equation in a small inelasticity regime in L1 spaces with polynomial weights. Finally, we study in the same and uniform framework from the spectral analysis point of view with a semigroup approach several Fokker-Planck equations which converge towards the classical one
Gautier, Eric. "Grandes déviations pour des équations de Schrödinger non linéaires stochastiques et applications." Phd thesis, 2005. http://tel.archives-ouvertes.fr/tel-00011274.
Full text