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Academic literature on the topic 'Partially Hyperbolic System'

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Published: 11 March 2023

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Journal articles on the topic "Partially Hyperbolic System"

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RIOS, I., and J. SIQUEIRA. "On equilibrium states for partially hyperbolic horseshoes." Ergodic Theory and Dynamical Systems 38, no. 1 (July 4, 2016): 301–35. http://dx.doi.org/10.1017/etds.2016.21.

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We prove the existence and uniqueness of equilibrium states for a family of partially hyperbolic systems, with respect to Hölder continuous potentials with small variation. The family comes from the projection, on the center-unstable direction, of a family of partially hyperbolic horseshoes introduced by Díaz et al [Destroying horseshoes via heterodimensional cycles: generating bifurcations inside homoclinic classes. Ergod. Th. & Dynam. Sys.29 (2009), 433–474]. For the original three-dimensional system we consider potentials with small variation, constant on local stable manifolds, obtaining existence and uniqueness of equilibrium states.
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RODRIGUEZ HERTZ, F., M. A. RODRIGUEZ HERTZ, A. TAHZIBI, and R. URES. "Maximizing measures for partially hyperbolic systems with compact center leaves." Ergodic Theory and Dynamical Systems 32, no. 2 (December 5, 2011): 825–39. http://dx.doi.org/10.1017/s0143385711000757.

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AbstractWe obtain the following dichotomy for accessible partially hyperbolic diffeomorphisms of three-dimensional manifolds having compact center leaves: either there is a unique entropy-maximizing measure, this measure has the Bernoulli property and its center Lyapunov exponent is 0, or there are a finite number of entropy-maximizing measures, all of them with non-zero center Lyapunov exponents (at least one with a negative exponent and one with a positive exponent), that are finite extensions of a Bernoulli system. In the first case of the dichotomy, we obtain that the system is topologically conjugated to a rotation extension of a hyperbolic system. This implies that the second case of the dichotomy holds for an open and dense set of diffeomorphisms in the hypothesis of our result. As a consequence, we obtain an open set of topologically mixing diffeomorphisms having more than one entropy-maximizing measure.
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ANDERSSON, MARTIN, and CARLOS H. VÁSQUEZ. "On mostly expanding diffeomorphisms." Ergodic Theory and Dynamical Systems 38, no. 8 (May 2, 2017): 2838–59. http://dx.doi.org/10.1017/etds.2017.17.

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In this work, we study the class of mostly expanding partially hyperbolic diffeomorphisms. We prove that such a class is$C^{r}$-open,$r>1$, among the partially hyperbolic diffeomorphisms and we prove that the mostly expanding condition guarantees the existence of physical measures and provides more information about the statistics of the system. Mañé’s classical derived-from-Anosov diffeomorphism on$\mathbb{T}^{3}$belongs to this set.
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Xu, Jiang, and Shuichi Kawashima. "Global Classical Solutions for Partially Dissipative Hyperbolic System of Balance Laws." Archive for Rational Mechanics and Analysis 211, no. 2 (October 8, 2013): 513–53. http://dx.doi.org/10.1007/s00205-013-0679-8.

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BUZZI, J., T. FISHER, M. SAMBARINO, and C. VÁSQUEZ. "Maximal entropy measures for certain partially hyperbolic, derived from Anosov systems." Ergodic Theory and Dynamical Systems 32, no. 1 (June 10, 2011): 63–79. http://dx.doi.org/10.1017/s0143385710000854.

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AbstractWe show that a class of robustly transitive diffeomorphisms originally described by Mañé are intrinsically ergodic. More precisely, we obtain an open set of diffeomorphisms which fail to be uniformly hyperbolic and structurally stable, but nevertheless have the following stability with respect to their entropy. Their topological entropy is constant and they each have a unique measure of maximal entropy with respect to which periodic orbits are equidistributed. Moreover, equipped with their respective measure of maximal entropy, these diffeomorphisms are pairwise isomorphic. We show that the method applies to several classes of systems which are similarly derived from Anosov, i.e. produced by an isotopy from an Anosov system, namely, a mixed Mañé example and one obtained through a Hopf bifurcation.
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Ondich, Jeffrey. "The reducibility of partially invariant solutions of systems of partial differential equations." European Journal of Applied Mathematics 6, no. 4 (August 1995): 329–54. http://dx.doi.org/10.1017/s0956792500001881.

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Ovsiannikov's partially invariant solutions of differential equations generalize Lie's group invariant solutions. A partially invariant solution is only interesting if it cannot be discovered more readily as an invariant solution. Roughly, a partially invariant solution that can be discovered more directly by Lie's method is said to be reducible. In this paper, I develop conditions under which a partially invariant solution or a class of such solutions must be reducible, and use these conditions both to obtain non-reducible solutions to a system of hyperbolic conservation laws, and to demonstrate that some systems have no non-reducible solutions. I also demonstrate that certain elliptic systems have no non-reducible solutions.
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Vergara-Hermosilla, G., G. Leugering, and Y. Wang. "Boundary controllability of a system modelling a partially immersed obstacle." ESAIM: Control, Optimisation and Calculus of Variations 27 (2021): 80. http://dx.doi.org/10.1051/cocv/2021076.

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In this paper, we address the problem of boundary controllability for the one-dimensional nonlinear shallow water system, describing the free surface flow of water as well as the flow under a fixed gate structure. The system of differential equations considered can be interpreted as a simplified model of a particular type of wave energy device converter called oscillating water column. The physical requirements naturally lead to the problem of exact controllability in a prescribed region. In particular, we use the concept of nodal profile controllability in which at a given point (the node) time-dependent profiles for the states are required to be reachable by boundary controls. By rewriting the system into a hyperbolic system with nonlocal boundary conditions, we at first establish the semi-global classical solutions of the system, then get the local controllability and nodal profile using a constructive method. In addition, based on this constructive process, we provide an algorithmic concept to calculate the required boundary control function for generating a solution for solving these control problem.
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Klar, A., and O. Tse. "An entropy functional and explicit decay rates for a nonlinear partially dissipative hyperbolic system." ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 95, no. 5 (March 10, 2014): 469–75. http://dx.doi.org/10.1002/zamm.201300275.

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GUPTA, CHINMAYA. "Extreme-value distributions for some classes of non-uniformly partially hyperbolic dynamical systems." Ergodic Theory and Dynamical Systems 30, no. 3 (July 17, 2009): 757–71. http://dx.doi.org/10.1017/s0143385709000406.

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AbstractIn this note, we obtain verifiable sufficient conditions for the extreme-value distribution for a certain class of skew-product extensions of non-uniformly hyperbolic base maps. We show that these conditions, formulated in terms of the decay of correlations on the product system and the measure of rapidly returning points on the base, lead to a distribution for the maximum of Φ(p)=−log(d(p,p0)) that is of the first type. In particular, we establish the type I distribution for S1 extensions of piecewise C2 uniformly expanding maps of the interval, non-uniformly expanding maps of the interval modeled by a Young tower, and a skew-product extension of a uniformly expanding map with a curve of neutral points.
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Rempel, M., and D. Przybylski. "Efficient Numerical Treatment of Ambipolar and Hall Drift as Hyperbolic System." Astrophysical Journal 923, no. 1 (December 1, 2021): 79. http://dx.doi.org/10.3847/1538-4357/ac2c6d.

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Abstract Partially ionized plasmas, such as the solar chromosphere, require a generalized Ohm’s law including the effects of ambipolar and Hall drift. While both describe transport processes that arise from the multifluid equations and are therefore of hyperbolic nature, they are often incorporated in models as a diffusive, i.e., parabolic process. While the formulation as such is easy to include in standard MHD models, the resulting diffusive time-step constraints do require often a computationally more expensive implicit treatment or super-time-stepping approaches. In this paper we discuss an implementation that retains the hyperbolic nature and allows for an explicit integration with small computational overhead. In the case of ambipolar drift, this formulation arises naturally by simply retaining a time derivative of the drift velocity that is typically omitted. This alone leads to time-step constraints that are comparable to the native MHD time-step constraint for a solar setup including the region from photosphere to lower solar corona. We discuss an accelerated treatment that can further reduce time-step constraints if necessary. In the case of Hall drift we propose a hyperbolic formulation that is numerically similar to that for the ambipolar drift and we show that the combination of both can be applied to simulations of the solar chromosphere at minimal computational expense.
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Dissertations / Theses on the topic "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.

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In the last years, an extremely powerful method has been developed: the functional approach. It consists in the study of the spectral properties of the transfer operators on suitable Banach spaces. In this work we apply this approach to partially hyperbolic systems in two dimensions, establishing the germ of a general theory. To illustrate the scope of the theory, the results are used in the case of fast-slow partially hyperbolic systems, pointing out how to pursue the arguments for further progresses.
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Ponce, 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/.

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Let f : T3 → T3 be a C2 volume preserving partially hyperbolic diffeomorphism homotopic to a linear Anosov automorphism A : T3 → T3. We prove that if f is Kolmogorov, then f is Bernoulli. We study the characteristics of atomic disintegration of the volume measure whenever it occurs. We prove that if the volume measure m has atomic disintegration on the center leaves then the disintegration has one atom per center leaf. We give a condition, depending only on the center Lyapunov exponent of the diffeomorphism, that guarantees atomic disintegration of the volume measure on center leaves. We construct an open family of diffeomorphisms satisfying this condition which generates the first examples of foliations which are both measurable and minimal. In this same construction we give the first examples of partially hyperbolic diffeomorphisms with zero center Lyapunov exponent and homotopic to a linear Anosov.
Seja 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.
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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/.

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Neste trabalho estudamos relações entre expoente de Lyapunov e continuidade absoluta da folheação central para difeomorfismos parcialmente hiperbólicos conservativos de \'T POT. 3\'. Sobre tal tema, provamos que tipicamente (\'C POT. 1\' aberto e \'C POT. 2\' denso) os difeomorfismos parcialmente hiperbólicos, conservativos de classe \'C POT. 2\' , do toro \'T POT. 3\', apresentam folheação central não absolutamente contínua. Desta maneira, respondemos positivamente uma pergunta proposta em [20]. Também neste trabalho, estudamos entropia topológica para Sistema Iterado de Funções. Neste contexto, damos uma nova demonstração para uma conjectura proposta em [14] e provada primeiramente em [15]. Apresentamos um método geométrico que nos permite calcular entropia para transformações de \'S POT. 1\', como em [15]. Além de disso o método apresentado se verifica para casos mais gerais, como por exemplo: transformações não comutativas
In 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
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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.

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Tese (doutorado) - Universidade Federal de Santa Catarina, Centro Tecnológico, Programa de Pós-Graduação em Engenharia de Automação e Sistemas, Florianópolis, 2017.
Made 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.
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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.

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Wir betrachten Optimalsteuerungsprobleme, die von partiellen Differentialgleichungen beziehungsweise Variationsungleichungen mit Differentialoperatoren erster Ordnung abhängen. Wir führen die Reformulierung eines Tagebauplanungsproblems, das auf stetigen Funktionen beruht, ein. Das Resultat ist ein Optimalsteuerungsproblem für Viskositätslösungen einer Eikonalgleichung. Die Existenz von Lösungen dieses und bestimmter Hilfsprobleme, die von semilinearen PDG‘s mit künstlicher Viskosität abhängen, wird bewiesen, Stationaritätsbedingungen hergeleitet und ein schwaches Konsistenzresultat für stationäre Punkte präsentiert. Des Weiteren betrachten wir Optimalsteuerungsprobleme, die von stationären Variationsungleichungen erster Art mit linearen Differentialoperatoren erster Ordnung abhängen. Wir diskutieren Lösbarkeit und Stationaritätskonzepte für diese Probleme. Für letzteres vergleichen wir Ergebnisse, die entweder durch die Anwendung von Penalisierungs- und Regularisierungsansätzen direkt auf Ebene von Differentialoperatoren erster Ordnung oder als Grenzwertprozess von Stationaritätssystemen für viskositätsregularisierte Optimalsteuerungsprobleme unter passenden Annahmen erhalten werden. Um die Konsistenz von ursprünglichem und regularisierten Problemen zu sichern, wird ein bekanntes Ergebnis für Lösungen von VU’s mit degeneriertem Differentialoperator erweitert. In beiden Fällen ist die erhaltene Stationarität schwächer als W-stationarität. Die theoretischen Ergebnisse werden anhand numerischer Beispiele verifiziert. Wir erweitern diese Ergebnisse auf Optimalsteuerungsprobleme bezüglich zeitabhängiger VU’s mit Differentialoperatoren erster Ordnung. Hierfür wird die Existenz von Lösungen bewiesen und erneut ein Stationaritätssystem mit Hilfe verschwindender Viskositäten unter bestimmten Beschränktheitsannahmen hergeleitet. Die erhaltenen Ergebnisse werden anhand von numerischen Beispielen verifiziert.
We 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.
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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.

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Haque, 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.

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Thesis (Ph.D. in Computational and Applied Mathematics)--S.M.U.
Title from PDF title page (viewed Mar. 16, 2009). Source: Dissertation Abstracts International, Volume: 69-08, Section: B Adviser: Peter K. Moore. Includes bibliographical references.
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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.

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Nguyen, Thi Hoai Thuong. "Numerical approximation of boundary conditions and stiff source terms in hyperbolic equations." Thesis, Rennes 1, 2020. http://www.theses.fr/2020REN1S027.

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Ce travail est consacré à l’étude théorique et numérique de systèmes hyperboliques d’équations aux dérivées partielles et aux équations de transport, avec des termes de relaxation et des conditions aux bords. Dans la première partie, on étudie la stabilité raide d’approximations numériques par différences finies du problème mixte donnée initiale-donnée au bord pour l’équation des ondes amorties dans le quart de plan. Dans le cadre du schéma discret en espace, nous proposons deux méthodes de discrétisation de la condition de Dirichlet. La première est la technique de sommation par partie et la seconde est basée sur le concept de condition au bord transparente. Nous proposons également une comparaison numérique des deux méthodes, en particulier de leur domaine de stabilité. La deuxième partie traite de schémas numériques d’ordre élevé pour l’équation de transport avec une donnée entrante sur domaine borné. Nous construisons, implémentons et analysons la procédure de Lax-Wendroff inverse au bord entrant. Nous obtenons des taux de convergence optimaux en combinant des estimations de stabilité précises pour l’extrapolation des conditions au bord avec des développements de couche limite numérique. Dans la dernière partie, nous étudions la stabilité de solutions stationnaires pour des systèmes non conservatifs avec des termes géométrique et de relaxation. Nous démontrons que les solutions stationnaires sont stables parmi les solutions entropique processus, qui généralisent le concept de solutions entropiques faibles. Nous supposons essentiellement que le système est complété par une entropie partiellement convexe et que, selon la dissipation du terme de relaxation, la stabilité ou la stabilité asymptotique des solutions stationnaires est obtenue
The 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
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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.

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Books on the topic "Partially Hyperbolic System"

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Nonlinear parabolic-hyperbolic coupled systems and their attractors. Basel: Birkhäuser, 2008.

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Qin, Yuming. Global Well-posedness of Nonlinear Parabolic-Hyperbolic Coupled Systems. Basel: Springer Basel, 2012.

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Roe, P. L. Discontinuous solutions to hyperbolic systems under operator splitting. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1987.

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D, Serre, ed. Multidimensional hyperbolic partial differential equations: First-order systems and applications. Oxford: Clarendon Press, 2007.

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A, Rand D., and Ferreira Flávio, eds. Fine structures of hyperbolic diffeomorphisms. Berlin: Springer, 2009.

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Hyperbolic partial differential equations and geometric optics. Providence, R.I: American Mathematical Society, 2012.

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Rhee, Hyun-Ku. Theory and application of hyperbolic systems of quasilinear equations. Englewood Cliffs, N.J: Prentice-Hall, 1989.

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Rhee, Hyun-Ku. Theory and application of hyperbolic systems of quasilinear equations. Mineola, N.Y: Dover Publications, 2001.

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V, Pogorelov Nikolai, and Semenov A. Yu 1955-, eds. Mathematical aspects of numerical solution of hyperbolic systems. Boca Raton: Chapman & Hall/CRC, 2001.

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(Albert), Milani A., ed. Linear and quasi-linear evolution equations in Hilbert spaces. Providence, R.I: American Mathematical Society, 2012.

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Book chapters on the topic "Partially Hyperbolic System"

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Kevorkian, J. "Quasilinear Hyperbolic Systems." In Partial Differential Equations, 386–457. Boston, MA: Springer US, 1990. http://dx.doi.org/10.1007/978-1-4684-9022-0_7.

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Ebert, Marcelo R., and Michael Reissig. "Linear Hyperbolic Systems." In Methods for Partial Differential Equations, 383–401. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-66456-9_22.

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Alinhac, Serge. "Operators and Systems in the Plane." In Hyperbolic Partial Differential Equations, 13–25. New York, NY: Springer New York, 2009. http://dx.doi.org/10.1007/978-0-387-87823-2_2.

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Alinhac, Serge. "Variable Coefficient Wave Equations and Systems." In Hyperbolic Partial Differential Equations, 111–36. New York, NY: Springer New York, 2009. http://dx.doi.org/10.1007/978-0-387-87823-2_7.

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Meister, Andreas, and Jens Struckmeier. "Central Schemes and Systems of Balance Laws." In Hyperbolic Partial Differential Equations, 59–114. Wiesbaden: Vieweg+Teubner Verlag, 2002. http://dx.doi.org/10.1007/978-3-322-80227-9_2.

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Bove, Antonio, and Tatsuo Nishitani. "Necessary Conditions for Hyperbolic Systems." In Partial Differential Equations and Mathematical Physics, 31–49. Boston, MA: Birkhäuser Boston, 2003. http://dx.doi.org/10.1007/978-1-4612-0011-6_3.

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Vârsan, C. "Bounded solutions for controlled hyperbolic systems." In Optimization, Optimal Control and Partial Differential Equations ISNM 107, 123–31. Basel: Birkhäuser Basel, 1992. http://dx.doi.org/10.1007/978-3-0348-8625-3_12.

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Gali, I. M., H. A. El-Saify, and S. A. El-Zahabi. "Optimal control of a system governed by hyperbolic operator." In Ordinary and Partial Differential Equations, 157–63. Berlin, Heidelberg: Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/bfb0074724.

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Bassanini, Piero, and Alan R. Elcrat. "Hyperbolic Systems of Conservation Laws in One Space Variable." In Theory and Applications of Partial Differential Equations, 291–394. Boston, MA: Springer US, 1997. http://dx.doi.org/10.1007/978-1-4899-1875-8_7.

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Marcati, Pierangelo. "Nonhomogeneous quasilinear hyperbolic systems: Initial and boundary value problem." In Calculus of Variations and Partial Differential Equations, 193–200. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/bfb0082896.

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Conference papers on the topic "Partially Hyperbolic System"

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LIVERANI, CARLANGELO. "TRANSPORT IN PARTIALLY HYPERBOLIC FAST-SLOW SYSTEMS." In International Congress of Mathematicians 2018. WORLD SCIENTIFIC, 2019. http://dx.doi.org/10.1142/9789813272880_0154.

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Wang, Xia, and Xiaodong Sun. "Hyperbolicity of One-Dimensional Two-Fluid Model With Interfacial Area Transport Equations." In ASME 2009 Fluids Engineering Division Summer Meeting. ASMEDC, 2009. http://dx.doi.org/10.1115/fedsm2009-78388.

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Two-fluid model with an empirical flow regime concept is widely used for two-phase flow analyses but suffers from its static and often non-hyperbolic nature. Recently, an interfacial area transport equation (IATE) has been proposed within the framework of the two-fluid model to dynamically describe the interfacial structure evolution and model the interfacial area concentration with the ultimate goal of modeling flow regime transition dynamically. Studies showed that the two-fluid model with the IATE (termed “two-fluid-IATE model” hereafter) could provide a more accurate prediction of the phase distributions and therefore improve the predictive capability of the two-fluid model. The inclusion of the IATE in the two-fluid model, however, brings about a subject of concern, namely, the well-posedness of the model. The objective of the present study is to investigate the issue of the hyperbolicity of a one-dimensional two-fluid-IATE model by employing momentum flux parameters, which take into account the coupling of the void fraction (volumetric fraction of the dispersed phase) and radial velocity distributions over the cross section of a flow passage. A characteristic analysis of the partial differential equations of the one-dimensional two-fluid model and two-group IATEs for an adiabatic flow was performed to identify a necessary condition for the system to achieve hyperbolicty. A case study was performed for an adiabatic liquid-liquid slug flow and the analysis showed that the hyperbolicty of the two-fluid-IATE model was guaranteed if appropriate correlations of the momentum flux parameters were applied in the two-fluid-IATE model.
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Vatankhah, Ramin, Mohammad Abediny, Hoda Sadeghian, and Aria Alasty. "Backstepping Boundary Control for Unstable Second-Order Hyperbolic PDEs and Trajectory Tracking." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-87038.

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In this paper, a problem of boundary feedback stabilization of second order hyperbolic partial differential equations (PDEs) is considered. These equations serve as a model for physical phenomena such as oscillatory systems like strings and beams. The controllers are designed using a backstepping method, which has been recently developed for parabolic PDEs. With the integral transformation and boundary feedback the unstable PDE is converted into a system which is stable in sense of Lyapunov. Then taylorian expansion is used to achieve the goal of trajectory tracking. It means design a boundary controller such that output of the system follows an arbitrary map. The designs are illustrated with simulations.
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Wadoo, Sabiha A. "Adaptive control of a hyperbolic Partial Differential Equation system with uncertain parameters." In 2012 15th International IEEE Conference on Intelligent Transportation Systems - (ITSC 2012). IEEE, 2012. http://dx.doi.org/10.1109/itsc.2012.6338718.

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Siranosian, Antranik A., Miroslav Krstic, Andrey Smyshlyaev, and Matt Bement. "Gain Scheduling-Inspired Control for Nonlinear Partial Differential Equations." In ASME 2009 Dynamic Systems and Control Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/dscc2009-2532.

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We present a control design method for nonlinear partial differential equations (PDEs) based on a combination of gain scheduling and backstepping theory for linear PDEs. A benchmark first-order hyperbolic system with a destabilizing in-domain nonlinearity is considered first. For this system a nonlinear feedback law based on gain scheduling is derived explicitly, and a statement of stability is presented for the closed-loop system. Control designs are then presented for a string and shear beam PDE, both with Kelvin-Voigt damping and potentially destabilizing free-end nonlinearities. String and beam simulation results illustrate the merits of the gain scheduling approach over the linearization-based design.
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Kholodov, Alexander S., and Yaroslav A. Kholodov. "Computational Models on Graphs for the Nonlinear Hyperbolic System of Equations." In ASME/JSME 2004 Pressure Vessels and Piping Conference. ASMEDC, 2004. http://dx.doi.org/10.1115/pvp2004-2580.

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The problems in the form of nonlinear partial derivative equations on graphs (nets, trees) arise in different applications. As the examples of such models we can name the circulatory and respiratory systems of the human body, the model of heavy traffic in the big cities, the model of flood water and pollution propagation in the large river systems, the model of bar structures and frames behavior under the different impacts, the model of the intensive information flows in the computer networks and others.
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Suzuki, Masayasu, Jun-ichi Imura, and Kazuyuki Aihara. "Controllability and observability of networked systems of linear hyperbolic partial differential equations." In 2011 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC 2011). IEEE, 2011. http://dx.doi.org/10.1109/cdc.2011.6161198.

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Liu, Shuyang, Reza Langari, and Yuanchun Li. "Control Design for the System of Manipulator Handling a Flexible Payload With Input Constraints." In ASME 2018 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/dscc2018-8970.

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In this paper, we consider the control design for manipulator handling a flexible payload in the presence of input constraints. The dynamics of the system is described by coupled ordinary differential equation and a partial differential equation. Considering actuators saturation, the proposed control law applies a smooth hyperbolic function to handle the effect of the input constraints. The asymptotic stability of the closed-loop system is proved by using semigroup theory and extended LaSalle’s Invariance Principle. Simulation results show that the proposed controller is effective.
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Danciu, Daniela. "Numerics for hyperbolic partial differential equations (PDE) via Cellular Neural Networks (CNN)." In 2013 2nd International Conference on Systems and Computer Science (ICSCS). IEEE, 2013. http://dx.doi.org/10.1109/icconscs.2013.6632044.

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Tsarev, Sergey P. "Generalized laplace transformations and integration of hyperbolic systems of linear partial differential equations." In the 2005 international symposium. New York, New York, USA: ACM Press, 2005. http://dx.doi.org/10.1145/1073884.1073929.

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Reports on the topic "Partially Hyperbolic System"

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Shearer, Michael. Systems of Hyperbolic Partial Differential Equations. Fort Belvoir, VA: Defense Technical Information Center, December 1994. http://dx.doi.org/10.21236/ada290287.

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Shearer, Michael. Systems of Nonlinear Hyperbolic Partial Differential Equations. Fort Belvoir, VA: Defense Technical Information Center, December 1997. http://dx.doi.org/10.21236/ada344449.

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