Дисертації з теми "Partially Hyperbolic System"
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CASTORRINI, ROBERTO. "Quantitative statistical properties for two dimensional partially hyperbolic systems." Doctoral thesis, Gran Sasso Science Institute, 2020. http://hdl.handle.net/20.500.12571/10321.
Повний текст джерелаPonce, Gabriel. "Fine ergodic properties of partially hyperbolic dynamical systems." Universidade de São Paulo, 2014. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-20032015-113539/.
Повний текст джерелаSeja f : T3 → T3 um difeomorfismo C2 parcialmente hiperbólico, homotópico a um automorfismo de Anosov linear e preservando a medida de volume m. Provamos que se f é Kolmogorov então f é Bernoulli. Estudamos as características da desintegração atômica da medida de volume quando esta ocorre. Provamos que se a medida de volume m tem desintegração atômica nas folhas centrais então a desintegração tem um átomo por folha central. Apresentamos uma condição, a qual depende apenas do expoente de Lyapunov central do difeomorfismo, que garante desintegração atômica da medida de volume. Construímos uma família aberta de difeomorfismos satisfazendo esta condição, o que gerou os primeiros exemplos de folheações que são mensuráveis e ao mesmo tempo minimais. Nesta mesma construção damos os primeiros exemplos de difeomorfismos parcialmente hiperbólicos com expoente de Lyapunov central nulo e homotópico a um Anosov linear.
Micena, Fernando Pereira. "Avanços em dinâmica parcialmente hiperbólica e entropia para sistema iterado de funções." Universidade de São Paulo, 2011. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-25042011-144207/.
Повний текст джерелаIn this work we study relations between Lyapunov exponents, absolute continuity of center foliation for conservative partially hyperbolic diffeomorphisms of \'T POT. 3\'. About this theme, (on a \'C POT. 1\' open and \'C POT. 2\'dense set) of conservative partially hyperbolic \'C POT. 2\' diffeomorphisms of the 3-torus presents non absolutely continuous center foliation. So, we answer positively a question proposed in [20]. Also in this work, we study topological entropy for Iterated Functions Systems. In this setting, we give a proof for a conjecture proposed in [14] and firstly proved in [15]. We present a geometrical method that allows us to calcule the entropy for transformations of \'S POT. 1\', like in [15]. Furthermore this method holds for more general cases, for example: non commutative transformations
Andrade, Gustavo Artur de. "Control of systems modeled by hyperbolic partial diferential equations." reponame:Repositório Institucional da UFSC, 2017. https://repositorio.ufsc.br/xmlui/handle/123456789/176753.
Повний текст джерелаMade available in DSpace on 2017-06-27T04:18:33Z (GMT). No. of bitstreams: 1 346334.pdf: 3570409 bytes, checksum: cf0611888dc2b3fb314d44683117c3fd (MD5) Previous issue date: 2017
Sistemas com parâmetros distribuídos representam uma vasta gama de processos da engenharia. Neste caso, as variáveis do sistema irão conter termos dependentes do tempo assim como gradientes espaciais e, portanto, é natural representa-los por equações diferenciais parciais. Exemplos podem ser encontrados em diversas áreas: desde processos químicos e térmicos, sistemas de produção e distribuição de energia, e problemas relacionados ao transporte de fluidos e ciência médica. Esta tese trata dois tipos de problemas: estabilização de equações diferenciais parciais lineares hiperbólicas com variável de controle na condição de contorno e controle regulatório de sistemas descritos por equações diferenciais parciais quasi-lineares hiperbólicas com variável de controle no domínio. Com relação ao primeiro, estudaram-se duas metodologias de controle: (i) uma lei de controle estática que garante convergência do sistema para o ponto de equilíbrio desejado. A metodologia de controle utiliza uma função de Lyapunov para encontrar os valores dos parâmetros do controlador que garantem estabilidade exponencial em malha fechada. Resultados de simulação para o problema de supressão de golfadas em sistemas de produção de petróleo são apresentados para ilustrar a eficiência do método; (ii) uma lei de controle baseada nas ferramentas clássicas do domínio da frequência. Neste caso, aplicamos a transformada de Laplace na equação diferencial parcial para obter uma função de transferência irracional e então, ferramentas clássicas do domínio da frequência são usadas para projetar o controlador, de maneira similar aos sistemas de dimensão finita com função de transferência racional. Estes resultados foram aplicados experimentalmente no problema de controle de oscilações termoacústicas do tubo de Rijke, mostrando a efetividade do método. Para o segundo problema, utiliza-se o método das características combinado com a técnica de controle por modos deslizantes. O método das características é usado para transformar o sistema de equações diferenciais parciais em um conjunto de equações diferenciais ordinárias que descrevem o sistema original. O projeto de controle é então realizado a partir deste conjunto de equações diferenciais ordinárias através de resultados bem conhecidos da teoria de equações diferenciais ordinárias. Os resultados obtidos foram testados experimentalmente em dois sistemas de escala industrial: uma planta solar e um fotobiorreator tubular.
Abstract : Distributed parameter systems represent a wide range of engineeringprocesses. In this case, the system variables will contain temporally dependentterms as well spatial gradients and, therefore, it is natural to representthem by partial dierential equations. Examples can be found in manyelds: chemical and thermal processes, production and distribution energysystems, and problems related to uid transport and medical science.This thesis deals with two dierent problems: stabilization of linear hyperbolicpartial dierential equations with boundary control and regulatorycontrol of systems described by quasilinear hyperbolic partial dierentialequations with in domain control. Concerning the boundary control problem,we studied two control methodologies: (i) a static control law thatguarantees convergence of the system to the desired equilibrium point. Thiscontrol methodology uses a Lyapunov function to nd the values of thecontrol parameters that guarantee closed-loop exponential stability. Simulationresults for the slugging control problem in oil production facilities arepresented to illustrate the eciency of the methodology; (ii) a control lawbased on the frequency domain tools. In this case, we applied the Laplacetransform on the partial dierential equation to obtain an irrational transferfunction and then classical frequency domain tools are used to designthe control law. These results were applied experimentally to the controlproblem of thermoacoustic oscillations in the Rijke tube, showing the effectivenessof the method. Regarding the regulatory control problem, weuse the method of characteristics together with the sliding mode controlmethodology. The method of characteristics is used to transform the partialdierential equations into a system of ordinary dierential equations thatdescribes the original system without any kind of approximation. Then,the control design is performed on the ordinary dierential equations withwell-known results of the theory of lumped parameter systems. The resultswere validated experimentally in two industrial scale systems: a solar powerplant and a tubular photobioreactor.
Strogies, Nikolai. "Optimization of nonsmooth first order hyperbolic systems." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät, 2016. http://dx.doi.org/10.18452/17633.
Повний текст джерелаWe consider problems of optimal control subject to partial differential equations and variational inequality problems with first order differential operators. We introduce a reformulation of an open pit mine planning problem that is based on continuous functions. The resulting formulation is a problem of optimal control subject to viscosity solutions of a partial differential equation of Eikonal Type. The existence of solutions to this problem and auxiliary problems of optimal control subject to regularized, semilinear PDE’s with artificial viscosity is proven. For the latter a first order optimality condition is established and a mild consistency result for the stationary points is proven. Further we study certain problems of optimal control subject to time-independent variational inequalities of the first kind with linear first order differential operators. We discuss solvability and stationarity concepts for such problems. In the latter case, we compare the results obtained by either utilizing penalization-regularization strategies directly on the first order level or considering the limit of systems for viscosity-regularized problems under suitable assumptions. To guarantee the consistency of the original and viscosity-regularized problems of optimal control, we extend known results for solutions to variational inequalities with degenerated differential operators. In both cases, the resulting stationarity concepts are weaker than W-stationarity. We validate the theoretical findings by numerical experiments for several examples. Finally, we extend the results from the time-independent to the case of problems of optimal control subject to VI’s with linear first order differential operators that are time-dependent. After establishing the existence of solutions to the problem of optimal control, a stationarity system is derived by a vanishing viscosity approach under certain boundedness assumptions and the theoretical findings are validated by numerical experiments.
Bohnet, Doris Verfasser], and Christian [Akademischer Betreuer] [Bonatti. "Partially hyperbolic systems with a compact center foliation with finite holonomy / Doris Bohnet. Betreuer: Christian Bonatti." Hamburg : Staats- und Universitätsbibliothek Hamburg, 2011. http://d-nb.info/1020466790/34.
Повний текст джерелаHaque, Md Z. "An adaptive finite element method for systems of second-order hyperbolic partial differential equations in one space dimension." Ann Arbor, Mich. : ProQuest, 2008. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3316356.
Повний текст джерелаTitle from PDF title page (viewed Mar. 16, 2009). Source: Dissertation Abstracts International, Volume: 69-08, Section: B Adviser: Peter K. Moore. Includes bibliographical references.
Kocoglu, Damla [Verfasser], and Stephan [Akademischer Betreuer] Trenn. "Analysis of Systems of Hyperbolic Partial Differential Equations Coupled to Switched Differential Algebraic Equations / Damla Kocoglu ; Betreuer: Stephan Trenn." Kaiserslautern : Technische Universität Kaiserslautern, 2021. http://d-nb.info/1224883853/34.
Повний текст джерелаNguyen, Thi Hoai Thuong. "Numerical approximation of boundary conditions and stiff source terms in hyperbolic equations." Thesis, Rennes 1, 2020. http://www.theses.fr/2020REN1S027.
Повний текст джерелаThe dissertation focuses on the study of the theoretical and numerical analysis of hyperbolic systems of partial differential equations and transport equations, with relaxation terms and boundary conditions. In the first part, we consider the stiff stability for numerical approximations by finite differences of the initial boundary value problem for the linear damped wave equation in a quarter plane. Within the framework of the difference scheme in space, we propose two methods of discretization of Dirichlet boundary condition. The first is the technique of summation by part and the second is based on the concept of transparent boundary conditions. We also provide a numerical comparison of the two numerical methods, in particular in terms of stability domain. The second part is about high order numerical schemes for transport equations with nonzero incoming boundary data on bounded domains. We construct, implement and analyze the so-called inverse Lax-Wendroff procedure at incoming boundary. We obtain optimal convergence rates by combining sharp stability estimate for extrapolation boundary conditions with numerical boundary layer expansions. In the last part, we study the stability of stationary solutions for non-conservative systems with geometric and relaxation source term. We prove that stationary solutions are stable among entropy process solution, which is a generalisation of the concept of entropy weak solutions. We mainly assume that the system is endowed with a partially convex entropy and, according to the entropy dissipation provided by the relaxation term, stability or asymptotic stability of stationary solutions is obtained
Sroczinski, Matthias [Verfasser]. "Global existence and asymptotic decay for quasilinear second-order symmetric hyperbolic systems of partial differential equations occurring in the relativistic dynamics of dissipative fluids / Matthias Sroczinski." Konstanz : KOPS Universität Konstanz, 2019. http://d-nb.info/1184795460/34.
Повний текст джерелаArnoldi, Jean-François. "Résonances de Ruelle à la limite semiclassique." Thesis, Grenoble, 2012. http://www.theses.fr/2012GRENM105/document.
Повний текст джерелаSince the work of Ruelle, then Rugh, Baladi, Tsujii, Liverani and others, it is kown that the convergence towards statistical equilibrium in many chaotic dynamical systems is gouverned by the Ruelle spectrum of resonances of the so-called transfer operator. Following recent works from Faure, Sjöstrand and Roy, this thesis gives a semiclassical approach for partially expanding chaotic dynamical systems. The first part of the thesis is devoted to compact Lie groups extenstions of expanding maps, essentially restricting to SU(2) extensions. Using Perlomov's coherent state theory for Lie groups, we apply the semiclassical theory of resonances of Helfer and Sjöstrand. We deduce Weyl type estimations and a spectral gap for the Ruelle resonances, showing that the convergence towards equilibrium is controled by a finite rank operator (as Tsujii already showed for partially expanding semi-flows). We then extend this approach to "open" models, for which the dynamics exhibits a fractal invariant reppeler. We show the existence of a discrete spectrum of resonances and we prove a fractal Weyl law, the classical analogue of Lin-Guillopé-Zworski's theorem on resonances of non-compact hyperbolic surfaces. We also show an asymptotic spectral gap. Finally we breifly explain why these models are interseting "toy models" to explore important questions of classical and quantum chaos. In particular, we have in mind the problem of proving lower bounds on the number of resonances, studied in the context of open quantum maps by Nonnenmacher and Zworski
Oliveira, Cleciano Berlando Miranda de. "Modelagem e simulação da propagação de ondas em barras não homogêneas envolvendo materiais elásticos não lineares." Universidade do Estado do Rio de Janeiro, 2012. http://www.bdtd.uerj.br/tde_busca/arquivo.php?codArquivo=4564.
Повний текст джерелаThe objective of this work is the simulation of the wave propagation phenomenon in a heterogeneous elastic rod, composed by two distinct materials (a linear and a non-linear one), each of them with its own wave propagation speed. At the interface between these materials there is a discontinuity, a stationary shock, due to the jump of the physical properties. Employing a reference configuration approach, a nonlinear hyperbolic system of partial differential equations, whose unknowns are the velocity and the strain, describing the dynamical response of the heterogeneous rod. The complete analytical solution of the associated Riemann problem is presented and discussed.
Bonnefille, Max. "Propagation des oscillations dans les systèmes hyperboliques de lois de conservation." Saint-Etienne, 1987. http://www.theses.fr/1987STET4008.
Повний текст джерелаLeguil, Martin. "Cocycle dynamics and problems of ergodicity." Thesis, Sorbonne Paris Cité, 2017. http://www.theses.fr/2017USPCC159/document.
Повний текст джерелаThe following work contains four chapters: the first one is centered around the weak mixing property for interval exchange transformations and translation flows. It is based on the results obtained together with Artur Avila which strengthen previous results due to Artur Avila and Giovanni Forni. The second chapter is dedicated to a joint work with Zhiyuan Zhang, in which we study the properties of stable ergodicity and accessibility for partially hyperbolic systems with center dimension at least two. We show that for dynamically coherent partially hyperbolic diffeomorphisms and under certain assumptions of center bunching and strong pinching, the property of stable accessibility is dense in C^r topology, r>1, and even prevalent in the sense of Kolmogorov. In the third chapter, we explain the results obtained together with Julie Déserti on the properties of a one-parameter family of polynomial automorphisms of C^3; we show that new behaviours can be observed in comparison with the two-dimensional case. In particular, we study the escape speed of points to infinity and show that a transition exists for a certain value of the parameter. The last chapter is based on a joint work with Jiangong You, Zhiyan Zhao and Qi Zhou; we get asymptotic estimates on the size of spectral gaps for quasi-periodic Schrödinger operators in the analytic case. We obtain exponential upper bounds in the subcritical regime, which strengthens a previous result due to Sana Ben Hadj Amor. In the particular case of almost Mathieu operators, we also show exponential lower bounds, which provides quantitative estimates in connection with the so-called "Dry ten Martinis problem". As consequences of our results, we show applications to the homogeneity of the spectrum of such operators, and to Deift's conjecture
Al, Zohbi Maryam. "Contributions to the existence, uniqueness, and contraction of the solutions to some evolutionary partial differential equations." Thesis, Compiègne, 2021. http://www.theses.fr/2021COMP2646.
Повний текст джерелаIn this thesis, we are mainly interested in the theoretical and numerical study of certain equations that describe the dynamics of dislocation densities. Dislocations are microscopic defects in materials, which move under the effect of an external stress. As a first work, we prove a global in time existence result of a discontinuous solution to a diagonal hyperbolic system, which is not necessarily strictly hyperbolic, in one space dimension. Then in another work, we broaden our scope by proving a similar result to a non-linear eikonal system, which is in fact a generalization of the hyperbolic system studied first. We also prove the existence and uniqueness of a continuous solution to the eikonal system. After that, we study this system numerically in a third work through proposing a finite difference scheme approximating it, of which we prove the convergence to the continuous problem, strengthening our outcomes with some numerical simulations. On a different direction, we were enthused by the theory of differential contraction to evolutionary equations. By introducing a new distance, we create a new family of contracting positive solutions to the evolutionary p-Laplacian equation
Roux, Raphaël. "Étude probabiliste de systèmes de particules en interaction : applications à la simulation moléculaire." Phd thesis, Université Paris-Est, 2010. http://tel.archives-ouvertes.fr/tel-00597479.
Повний текст джерелаTalitskaya, Anna. "Partially hyperbolic phenomena in dynamical systems with discrete and continuous time." 2004. http://etda.libraries.psu.edu/theses/approved/WorldWideIndex/ETD-533/index.html.
Повний текст джерелаBohnet, Doris. "Partially hyperbolic diffeomorphisms with a compact center foliation with finite holonomy." Phd thesis, 2011. http://tel.archives-ouvertes.fr/tel-00782664.
Повний текст джерелаCarrasco, Correa Pablo Daniel. "Compact Dynamical Foliations." Thesis, 2011. http://hdl.handle.net/1807/27574.
Повний текст джерела李權育, Quan-Yu Li, and 李權育. "A Sampled-Data Formulation for Boundary Control of a Hyperbolic Partial Differential Equation System." Thesis, 2012. http://ndltd.ncl.edu.tw/handle/04974206573132392169.
Повний текст джерела國立中興大學
電機工程學系所
100
This thesis presents an analytic solution to the hyperbolic partial differential equation systems. Obvious, the partial differential equations are more difficult than the ordinary differential equations system for study. Therefore, this thesis proposed a sample-data formulation to analytic solution to the boundary hyperbolic partial differential equation systems. With boundary conditions satisfying the regular form of Strum-Liouville problem, and used the eigenfunctions expansion method to making hyperbolic partial differential equation into an infinite sequence of discrete-time control problems. The finite-dimensional approximation of the discrete-time system is obtained by the minimum square error theorem of Fourier series. And this thesis for verification to the proposed analysis derivation of the equation result. Therefore, to introduce two numerical analysis simulation methods, ones are direct to used finite difference approximate method to solve hyperbolic partial differential equation systems, and the other ones are use proposed sampled-data formulation of finite-dimensional discrete-time system control. In the end, to compare our proposed method with finite difference approximate method for to verification this proposed method feasibility.
Michaud, Matthieu. "Schéma implicite pour la résolution d'un système hyperbolique d'équations aux dérivées partielles." Thèse, 2002. http://hdl.handle.net/1866/14607.
Повний текст джерелаHante, Falk Michael [Verfasser]. "Hybrid dynamics comprising modes governed by partial differential equations : modeling, analysis and control for semilinear hyperbolic systems in one space dimension / vorgelgt von Falk Michael Hante." 2010. http://d-nb.info/1006656782/34.
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