Relevant bibliographies by topics / Semigroup stability

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Semigroup stability'

Author: Grafiati
Published: 4 June 2021
Last updated: 4 February 2022

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Journal articles on the topic "Semigroup stability"

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Bodor, Bertalan, Erkko Lehtonen, Thomas Quinn-Gregson, and Nikolaas Verhulst. "HS-stability and complex products in involution semigroups." Semigroup Forum 103, no. 2 (August 10, 2021): 395–413. http://dx.doi.org/10.1007/s00233-021-10213-x.

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AbstractWhen does the complex product of a given number of subsets of a group generate the same subgroup as their union? We answer this question in a more general form by introducing HS-stability and characterising the HS-stable involution subsemigroup generated by a subset of a given involution semigroup. We study HS-stability for the special cases of regular $${}^{*}$$ ∗ -semigroups and commutative involution semigroups.
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Chill, R., D. Seifert, and Y. Tomilov. "Semi-uniform stability of operator semigroups and energy decay of damped waves." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 378, no. 2185 (October 19, 2020): 20190614. http://dx.doi.org/10.1098/rsta.2019.0614.

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Only in the last 15 years or so has the notion of semi-uniform stability, which lies between exponential stability and strong stability, become part of the asymptotic theory of C 0 -semigroups. It now lies at the very heart of modern semigroup theory. After briefly reviewing the notions of exponential and strong stability, we present an overview of some of the best known (and often optimal) abstract results on semi-uniform stability. We go on to indicate briefly how these results can be applied to obtain (sometimes optimal) rates of energy decay for certain damped second-order Cauchy problems. This article is part of the theme issue ‘Semigroup applications everywhere’.
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Han, Xiaoshuang, Mingyan Teng, and Ming Fang. "Well-posedness and Stability of the Repairable System with Three Units and Vacation." Journal of Systems Science and Information 2, no. 1 (February 25, 2014): 54–76. http://dx.doi.org/10.1515/jssi-2014-0054.

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AbstractThe stability of the repairable system with three units and vacation was investigated by two different methods in this note. The repairable system is described by a set of ordinary differential equation coupled with partial differential equations with initial values and integral boundaries. To apply the theory of positive operator semigroups to discuss the repairable system, the system equations were transformed into an abstract Cauchy problem on some Banach lattice. The system equations have a unique non-negative dynamic solution and positive steady-state solution and dynamic solution strongly converges to steady-state solution were shown on the basis of the detailed spectral analysis of the system operator. Furthermore, the Cesáro mean ergodicity of the semigroupT(t) generated by the system operator was also shown through the irreducibility of the semigroup.
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Xueli, Song, and Peng Jigen. "Equivalence of Lp Stability and Exponential Stability of Nonlinear Lipschitzian Semigroups." Canadian Mathematical Bulletin 55, no. 4 (December 1, 2012): 882–89. http://dx.doi.org/10.4153/cmb-2011-070-0.

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AbstractLp stability and exponential stability are two important concepts for nonlinear dynamic systems. In this paper, we prove that a nonlinear exponentially bounded Lipschitzian semigroup is exponentially stable if and only if the semigroup is Lp stable for some p > 0. Based on the equivalence, we derive two sufficient conditions for exponential stability of the nonlinear semigroup. The results obtained extend and improve some existing ones.
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Soliman, Ahmed. "A common fixed point theorem for semigroups of nonlinear uniformly continuous mappings with an application to asymptotic stability of nonlinear systems." Filomat 31, no. 7 (2017): 1949–57. http://dx.doi.org/10.2298/fil1707949s.

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In this paper, we study the existence of a common fixed point for uniformly continuous one parameter semigroups of nonlinear self-mappings on a closed convex subset C of a real Banach space X with uniformly normal structure such that the semigroup has a bounded orbit. This result applies, in particular, to the study of an asymptotic stability criterion for a class of semigroup of nonlinear uniformly continuous infinite-dimensional systems.
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Acu, Ana Maria, and Ioan Raşa. "A C0-Semigroup of Ulam Unstable Operators." Symmetry 12, no. 11 (November 7, 2020): 1844. http://dx.doi.org/10.3390/sym12111844.

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The Ulam stability of the composition of two Ulam stable operators has been investigated by several authors. Composition of operators is a key concept when speaking about C0-semigroups. Examples of C0-semigroups formed with Ulam stable operators are known. In this paper, we construct a C0-semigroup (Rt)t≥0 on C[0,1] such that for each t>0, Rt is Ulam unstable. Moreover, we compute the central moments of Rt and establish a Voronovskaja-type formula. This enables to prove that C2[0,1] is contained in the domain D(A) of the infinitesimal generator of the semigroup. We raise the problem to fully characterize the domain D(A).
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Bobrowski, Adam, and Ryszard Rudnicki. "On convergence and asymptotic behaviour of semigroups of operators." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 378, no. 2185 (October 19, 2020): 20190613. http://dx.doi.org/10.1098/rsta.2019.0613.

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The classical and modern theorems on convergence, approximation and asymptotic stability of semigroups of operators are presented, and their applications to recent biological models are discussed. This article is part of the theme issue ‘Semigroup applications everywhere’.
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Braga Barros, Carlos J., Josiney A. Souza, and Victor H. L. Rocha. "Lyapunov stability for semigroup actions." Semigroup Forum 88, no. 1 (October 24, 2013): 227–49. http://dx.doi.org/10.1007/s00233-013-9527-2.

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Kumar, Dharmendra, Kalyan B. Sinha, and Sachi Srivastava. "Stability of the Markov (conservativity) property under perturbations." Infinite Dimensional Analysis, Quantum Probability and Related Topics 23, no. 02 (June 2020): 2050009. http://dx.doi.org/10.1142/s0219025720500095.

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Sun, Xi Ping, Min Luo, and Kai Fang. "A Continuous Semigroup Approach to the Distributional Stability of Nonlinear Models." Applied Mechanics and Materials 525 (February 2014): 653–56. http://dx.doi.org/10.4028/www.scientific.net/amm.525.653.

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We prove the existence of an invariant measure for the continuous semigroup associate with a nonlinear model under the compact set Lyapunov condition. Further,adding the ergodicity of the semigroup operator, we prove the asymptotic stability in distribution for the semigroup. We give a criteria of the asymptotic stability in distribution for the type of evolution equation having a linear generator. Our method is based on continuous semigroup and its generator.We illustrate the result by the Lorenz chaotic model and prove the existence of the natural invariant measure for Lorenz chaotic model.
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Dissertations / Theses on the topic "Semigroup stability"

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Aroza, Benlloch Javier. "Dynamics of strongly continuous semigroups associated to certain differential equations." Doctoral thesis, Universitat Politècnica de València, 2015. http://hdl.handle.net/10251/57186.

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[EN] The purpose of the Ph.D. Thesis "Dynamics of strongly continuous semigroups associated to certain differential equations'' is to analyse, from the point of view of functional analysis, the dynamics of solutions of linear evolution equations. These solutions can be represented by a strongly continuous semigroup on an infinite-dimensional Banach space. The aim of our research is to provide global conditions for chaos, in the sense of Devaney, and stability properties of strongly continuous semigroups which are solutions of linear evolution equations. This work is composed of three principal chapters. Chapter 0 is introductory and defines basic terminology and notation used, besides presenting the basic results that we will use throughout this thesis. Chapters 1 and 2 describe, in general way, a strongly continuous semigroup induced by a semiflow in Lebesgue and Sobolev spaces which is a solution of a linear first order partial differential equation. Moreover, some characterizations of the main dynamical properties, including hypercyclicity, mixing, weakly mixing, chaos and stability are given along these chapters. Chapter 3 describes the dynamical properties of a difference equation based on the so-called birth-and-death model and analyses the conditions previously proven for this model improving them by employing a different strategy. The goal of this thesis is to characterize dynamical properties of these kind of strongly continuous semigroups in a general way, whenever possible, and to extend these results to another spaces. Along this memory, these findings are compared with the previous ones given by many authors in recent years.
[ES] La presente memoria "Dinámica de semigrupos fuertemente continuos asociadas a ciertas ecuaciones diferenciales'' es analizar, desde el punto de vista del análisis funcional, la dinámica de las soluciones de ecuaciones de evolución lineales. Estas soluciones pueden ser representadas por semigrupos fuertemente continuos en espacios de Banach de dimensión infinita. El objetivo de nuestra investigación es proporcionar condiciones globales para obtener caos, en el sentido de Devaney, y propiedades de estabilidad de semigrupos fuertemente continuos, los cuales son soluciones de ecuaciones de evolución lineales. Este trabajo está compuesto de tres capítulos principales. El Capítulo 0 es introductorio y define la terminología básica y notación usada, además de presentar los resultados básicos que usaremos a lo largo de esta tesis. Los Capítulos 1 y 2 describen, de forma general, un semigrupo fuertemente continuo inducido por un semiflujo en espacios de Lebesgue y en espacios de Sobolev, los cuales son solución de una ecuación diferencial lineal en derivadas parciales de primer orden. Además, algunas caracterizaciones de las principales propiedades dinámicas, incluyendo hiperciclicidad, mezclante, débil mezclante, caos y estabilidad, se obtienen a lo largo de estos capítulos. El Capítulo 3 describe las propiedades dinámicas de una ecuación en diferencias basada en el llamado modelo de nacimiento-muerte y analiza las condiciones previamente probadas para este modelo, mejorándolas empleando una estrategia diferente. La finalidad de esta tesis es caracterizar propiedades dinámicas para este tipo de semigrupos fuertemente continuos de forma general, cuando sea posible, y extender estos resultados a otros espacios. A lo largo de esta memoria, estos resultados son comparados con los resultados previos dados por varios autores en años recientes.
[CAT] La present memòria "Dinàmica de semigrups fortament continus associats a certes equacions diferencials'' és analitzar, des del punt de vista de l'anàlisi funcional, la dinàmica de les solucions d'equacions d'evolució lineals. Aquestes solucions poden ser representades per semigrups fortament continus en espais de Banach de dimensió infinita. L'objectiu de la nostra investigació es proporcionar condicions globals per obtenir caos, en el sentit de Devaney, i propietats d'estabilitat de semigrups fortament continus, els quals són solucions d'equacions d'evolució lineals. Aquest treball està compost de tres capítols principals. El Capítol 0 és introductori i defineix la terminologia bàsica i notació utilitzada, a més de presentar els resultats bàsics que utilitzarem al llarg d'aquesta tesi. Els Capítols 1 i 2 descriuen, de forma general, un semigrup fortament continu induït per un semiflux en espais de Lebesgue i en espais de Sobolev, els quals són solució d'una equació diferencial lineal en derivades parcials de primer ordre. A més, algunes caracteritzacions de les principals propietats dinàmiques, incloent-hi hiperciclicitat, mesclant, dèbil mesclant, caos i estabilitat, s'obtenen al llarg d'aquests capítols. El Capítol 3 descrivís les propietats dinàmiques d'una equació en diferències basada en el model de naixement-mort i analitza les condicions prèviament provades per aquest model, millorant-les utilitzant una estratègia diferent. La finalitat d'aquesta tesi és caracteritzar propietats dinàmiques d'aquest tipus de semigrups fortament continus de forma general, quan siga possible, i estendre aquests resultats a altres espais. Al llarg d'aquesta memòria, aquests resultats són comparats amb els resultats previs obtinguts per diversos autors en anys recents.
Aroza Benlloch, J. (2015). Dynamics of strongly continuous semigroups associated to certain differential equations [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/57186
TESIS
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Mulzet, Alfred Kenric. "Exponential Stability for a Diffusion Equation in Polymer Kinetic Theory." Diss., Virginia Tech, 1997. http://hdl.handle.net/10919/30473.

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In this paper we present an exponential stability result for a diffusion equation arising from dumbbell models for polymer flow. Using the methods of semigroup theory, we show that the semigroup U(t) associated with the diffusion equation is well defined and that all solutions converge exponentially to an equilibrium solution. Both finitely and infinitely extensible dumbbell models are considered. The main tool in establishing stability is the proof of compactness of the semigroup.
Ph. D.
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Song, Degong. "On the Spectrum of Neutron Transport Equations with Reflecting Boundary Conditions." Diss., Virginia Tech, 2000. http://hdl.handle.net/10919/26375.

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This dissertation is devoted to investigating the time dependent neutron transport equations with reflecting boundary conditions. Two typical geometries --- slab geometry and spherical geometry --- are considered in the setting of L^p including L^1. Some aspects of the spectral properties of the transport operator A and the strongly continuous semigroup T(t) generated by A are studied. It is shown under fairly general assumptions that the accumulation points of { m Pas}(A):=sigma (A) cap { lambda :{ m Re}lambda > -lambda^{ast} }, if they exist, could only appear on the line { m Re}lambda =-lambda^{ast}, where lambda^{ast} is the essential infimum of the total collision frequency. The spectrum of T(t) outside the disk {lambda : |lambda| leq exp (-lambda^{ast} t)} consists of isolated eigenvalues of T(t) with finite algebraic multiplicity, and the accumulation points of sigma (T(t)) igcap{ lambda : |lambda| > exp (-lambda^{ast} t)}, if they exist, could only appear on the circle {lambda :|lambda| =exp (-lambda^{ast} t)}. Consequently, the asymptotic behavior of the time dependent solution is obtained.
Ph. D.
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Schulze, Bert-Wolfgang, and Yuming Qin. "Uniform compact attractors for a nonlinear non-autonomous equation of viscoelasticity." Universität Potsdam, 2005. http://opus.kobv.de/ubp/volltexte/2009/2989/.

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In this paper we establish the regularity, exponential stability of global (weak) solutions and existence of uniform compact attractors of semiprocesses, which are generated by the global solutions, of a two-parameter family of operators for the nonlinear 1-d non-autonomous viscoelasticity. We employ the properties of the analytic semigroup to show the compactness for the semiprocess generated by the global solutions.
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Ghader, Mouhammad. "Stabilité et contrôlabilité exacte des systèmes distribués couplés avec différents types d'amortissement." Thesis, Université Paris-Saclay (ComUE), 2018. http://www.theses.fr/2018SACLS078.

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Dans cette thèse, nous étudions la stabilisation et la contrôlabilité exacte de certains problèmes distribués avec différents types d’amortissement. Dans la première partie, nous étudions la stabilité d'un système Bresse mono-dimensionnel avec un contrôle de type mémoire infini et/ou avec une conduction de chaleur donnée par la loi de Cattaneo agissant sur le déplacement de l'angle de cisaillement. Nous considérons le cas intéressant de conditions aux bords de types entièrement Dirichlet. En effet, sous la condition d'égalité de la vitesse de propagation des ondes, nous établissons la stabilité exponentielle du système. Cependant, dans le cas physique naturel lorsque les vitesses de propagation sont différentes, en utilisant une méthode de décomposition de spectre, nous montrons que le système de Bresse n'est pas uniformément stable. Dans ce cas, nous établissons un taux de décroissance énergétique polynomiale. Notre étude est valable pour toutes les autres conditions aux bords mixtes. Dans la deuxième partie, nous étudions la stabilisation d'un système élastique faiblement amorti d’un système couplé abstrait du second ordre. Dans le cadre de certains paramètres, en utilisant la méthode spectrale, nous établissons la stabilité exponentielle du système. Cependant, lorsque le système n'est pas uniformément stable, nous établissons le taux optimal de la décroissance polynomiale de l'énergie du système. Dans la troisième partie, nous étudions la contrôlabilité exacte indirecte d'un système de Timoshenko mono-dimensionnel. En effet, nous considérons les cas lorsque la vitesse de propagation des ondes sont égales ou différentes. Tout d'abord, nous utilisons des analyses non harmoniques pour établir une inégalité d'observabilité faible, qui dépend du rapport des vitesses de propagation des ondes. Ensuite, en utilisant la méthode HUM, nous prouvons que le Système est parfaitement contrôlable et que le temps de contrôle peut être faible
In this work, we study the stabilization and the exact controllability of some distributed problems. In the first part, we study the stability of a one-dimensional Bresse System with infinite memory type control and/or with heat conduction given by Cattaneo's law acting in the shear angle displacement, where we consider the interesting case of fully Dirichlet boundary conditions. Indeed, under a equal speed of propagation condition, we establish the exponential stability of the System. However, in the natural physical case when the speeds of propagation are different, using a spectrum method, we show that the Bresse System is not uniformly exponentially stable. In this case, we establish a polynomial energy decay rate. Our study is valid for all other mixed boundary conditions. In the second part, we study the stabilization of a weakly damped elastic System of an abstract second order equation. Indeed, under some condition on the parameters, using a spectrum method, we establish the exponential stability of the System. However, when the System is not uniformly stable, using a spectrum method, we establish the optimal polynomial decay rate of the energy of the System. In the third part, we study the indirect boundary exact controllability of a one-dimensional Timoshenko System. Indeed, we consider the cases when the speed waves propagate with equal or different speeds. We use non harmonic analysis to establish weak observability inequality, which depends on the ratio of the waves propagation speeds. Next, using the HUM method, we prove that the System is exactly controllable, and that the control time can be small
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Pena, Ismael da Silva [UNESP]. "Análise de estabilidade de sistemas dinâmicos híbridos e descontínuos modelados por semigrupos:." Universidade Estadual Paulista (UNESP), 2008. http://hdl.handle.net/11449/94205.

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Made available in DSpace on 2014-06-11T19:26:55Z (GMT). No. of bitstreams: 0 Previous issue date: 2008-02-26Bitstream added on 2014-06-13T18:30:53Z : No. of bitstreams: 1 pena_is_me_sjrp.pdf: 488383 bytes, checksum: 40a97f3540caa6b8f6f2691c3a402579 (MD5)
Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
Sistemas dinâmicos híbridos se diferenciam por exibir simultaneamente variados tipos de comportamento dinâmico (contínuo, discreto, eventos discretos) em diferentes partes do sistema. Neste trabalho foram estudados resultados de estabilidade no sentido de Lyapunov para sistemas dinâmicos híbridos gerais, que utilizam uma noção de tempo generalizado, definido em um espaço métrico totalmente ordenado. Mostrou-se que estes sistemas podem ser imersos em sistemas dinâmicos descontínuos definidos em R+, de forma que sejam preservadas suas propriedades qualitativas. Como foco principal, estudou-se resultados de estabilidade para sistemas dinâmicos descontínuos modelados por semigrupos de operadores, em que os estados do sistema pertencem à espaços de Banach. Neste caso, de forma alternativa à teoria clássica de estabilidade, os resultados não utilizam as usuais funções de Lyapunov, sendo portanto mais fáceis de se aplicar, tendo em vista a dificuldade em se encontrar tais funções para muitos sistemas. Além disso, os resultados foram aplicados à uma classe de equações diferenciais com retardo.
Hybrid dynamical systems are characterized for showing simultaneously a variety of dynamic behaviors (continuous, discrete, discrete events) in different parts of the System. This work discusses stability results in the Lyapunov sense for general hybrid dynamical systems that use a generalized notion of time, defined in a completely ordered metric space. It has been shown that these systems may be immersed in discontinuous dynamical systems defined in R+, so that their quality properties are preserved. As the main focus, it is studied stability results for discontinuous dynamical systems modeled by semigroup operators, in which the states belong to Banach spaces. In this case, an alternative to the classical theory of stability, the results do not make use of the usual Lyapunov functions, and therefore are easier to apply, in view of the difficulty in finding such functions for many systems. Furthermore, the results were applied to a class of time-delay discontinuous differential equations.
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Fischer, Arthur Geromel. "Robustez da dinâmica sob perturbações: da semicontinuidade superior à estabilidade estrutural." Universidade de São Paulo, 2015. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-08012016-110211/.

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O objetivo principal deste trabalho é o estudo da estabilidade estrutural dos atratores de semigrupos. Começamos este trabalho apresentando o conceito e propriedades básicas de semigrupos que possuem atratores globais. Estudamos, então, semigrupos gradientes e dinamicamente gradientes, mostrando que eles são equivalentes e que uma pequena perturbação autônoma de um semigrupo gradiente continua sendo gradiente. Estudamos as variedades estável e instável de um ponto de equilíbrio hiperbólico e o comportamento de soluções periódicas sob perturbação. Concluímos este trabalho com o estudo dos semigrupos Morse-Smale.
The main goal of this work is the study of structural stability of global attractors. We start this work by presenting the concept and basic properties of semigroups and global attractors. We then studied gradient and dinamically gradient semigroups, showing that these concepts are equivalent and that a small autonomous pertubation of a gradient semigroup remains a gradient semigroup. We studied the stable and unstable manifolds in the neighbourhood of a hyperbolic equilibrium point and the behavior of periodic solutions under perturbation. Finally, we studied the Morse-Smale semigroups.
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Tchousso, Abdoua. "Étude de la stabilité asymptotique de quelques modèles de transfert de chaleur." Lyon 1, 2004. http://www.theses.fr/2004LYO10119.

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Notre mémoire de thèse porte sur l'étude de la stabilité asymptotique principalement exponentielle de quelques problèmes de type paraboliques ou hyperboliques d'ordre un, modélisant des phénomènes de transfert de chaleur. Nous présentons tout d'abord des rappels de notions connues, utiles dans la suite du travail. Ces rappels concernent des théorèmes d'analyse fonctionnelle, des propriétés spectrales d'opérateurs linéaires, la théorie des semi-groupes continus et analytiques et les équations d'évolutions linéaires et semi-linéaires. Nous traitons ensuite de la stabilité exponentielle et du comportement asymptotique des modèles 1-phase et 2-phase du procédé de transfert de chaleur à lits fixes en utilisant la méthode de Lyapunov. Après avoir prouvé, par une méthode directe, l'égalité du taux de décroissance exponentielle et de la borne spectrale pour le modèle 1-phase, nous déterminons sa région de stabilité exponentielle. En troisième point, nous établissons par une démarche simple des résultats techniques d'analyticité et de compacité pour les semi-groupes associés aux systèmes. En quatrième point, nous étudions la stabilité exponentielle du réseau d'échangeurs thermiques avec ou sans diffusion dans divers espaces de Banach. En cinquième point, nous proposons une approche de Lyapunov pour prouver la stabilité exponentielle du système hyperbolique symétrique. Enfin, nous utilisons des résultats de compacité du semi-groupe pour étudier le comportement asymptotique des solutions d'équations et systèmes d'équations semi-linéaires
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Pace, Michele. "Stochastic models and methods for multi-object tracking." Phd thesis, Université Sciences et Technologies - Bordeaux I, 2011. http://tel.archives-ouvertes.fr/tel-00651396.

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La poursuite multi-cibles a pour objet le suivi d'un ensemble de cibles mobiles à partir de données obtenues séquentiellement. Ce problème est particulièrement complexe du fait du nombre inconnu et variable de cibles, de la présence de bruit de mesure, de fausses alarmes, d'incertitude de détection et d'incertitude dans l'association de données. Les filtres PHD (Probability Hypothesis Density) constituent une nouvelle gamme de filtres adaptés à cette problématique. Ces techniques se distinguent des méthodes classiques (MHT, JPDAF, particulaire) par la modélisation de l'ensemble des cibles comme un ensemble fini aléatoire et par l'utilisation des moments de sa densité de probabilité. Dans la première partie, on s'intéresse principalement à la problématique de l'application des filtres PHD pour le filtrage multi-cibles maritime et aérien dans des scénarios réalistes et à l'étude des propriétés numériques de ces algorithmes. Dans la seconde partie, nous nous intéressons à l'étude théorique des processus de branchement liés aux équations du filtrage multi-cibles avec l'analyse des propriétés de stabilité et le comportement en temps long des semi-groupes d'intensités de branchements spatiaux. Ensuite, nous analysons les propriétés de stabilité exponentielle d'une classe d'équations à valeurs mesures que l'on rencontre dans le filtrage non-linéaire multi-cibles. Cette analyse s'applique notamment aux méthodes de type Monte Carlo séquentielles et aux algorithmes particulaires dans le cadre des filtres de Bernoulli et des filtres PHD.
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Tristani, Isabelle. "Existence et stabilité de solutions fortes en théorie cinétique des gaz." Thesis, Paris 9, 2015. http://www.theses.fr/2015PA090013/document.

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Cette thèse est centrée sur l’étude d’équations issues de la théorie cinétique des gaz. Dans tous les problèmes qui y sont explorés, une analyse des problèmes linéaires ou linéarisés associés est réalisée d’un point de vue spectral et du point de vue des semi-groupes. A cela s’ajoute une analyse de la stabilité non linéaire lorsque le modèle est non linéaire. Plus précisément, dans une première partie, nous nous intéressons aux équations de Fokker-Planck fractionnaire et Boltzmann sans cut-off homogène en espace et nous prouvons un retour vers l’équilibre des solutions de ces équations avec un taux exponentiel dans des espaces de type L1 à poids polynomial. Concernant l’équation de Landau inhomogène en espace, nous développons une théorie de Cauchy de solutions perturbatives dans des espaces de type L2 avec différents poids (polynomiaux ou exponentiels) et nous prouvons également la stabilité exponentielle de ces solutions.Nous démontrons ensuite pour l’équation de Boltzmann inélastique inhomogène avec terme diffusif le même type de résultat dans des espaces L1 à poids polynomial dans un régime de faible inélasticité. Pour finir, nous étudions dans un cadre général et uniforme des modèles qui convergent vers l’équation de Fokker-Planck du point de vue de l’analyse spectrale et des semi-groupes
The 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
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Books on the topic "Semigroup stability"

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Eisner, Tanja. Stability of Operators and Operator Semigroups. Basel: Springer Basel, 2010. http://dx.doi.org/10.1007/978-3-0346-0195-5.

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Eisner, Tanja. Stability of operators and operator semigroups. Basel: Birkhäuser, 2010.

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Eisner, Tanja. Stability of operators and operator semigroups. Basel: Birkhäuser, 2010.

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Eisner, Tanja. Stability of Operators and Operator Semigroups. Birkhäuser, 2012.

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Book chapters on the topic "Semigroup stability"

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Bucci, Francesca. "Stability of Holomorphic Semigroup Systems under Nonlinear Boundary Perturbations." In Optimal Control of Partial Differential Equations, 63–76. Basel: Birkhäuser Basel, 1999. http://dx.doi.org/10.1007/978-3-0348-8691-8_6.

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Neustupa, Jiří. "Stability of Solutions of Parabolic Equations by a Combination of the Semigroup Theory and the Energy Method." In Navier—Stokes Equations and Related Nonlinear Problems, 11–22. Boston, MA: Springer US, 1995. http://dx.doi.org/10.1007/978-1-4899-1415-6_2.

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Eisner, Tanja. "Stability of C0-semigroups." In Stability of Operators and Operator Semigroups, 79–132. Basel: Springer Basel, 2010. http://dx.doi.org/10.1007/978-3-0346-0195-5_3.

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Luo, Zheng-Hua, Bao-Zhu Guo, and Omer Morgul. "Stability of C0-Semigroups." In Stability and Stabilization of Infinite Dimensional Systems with Applications, 109–64. London: Springer London, 1999. http://dx.doi.org/10.1007/978-1-4471-0419-3_3.

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Gil’, Michael I. "Strongly Continuous Semigroups." In Stability of Finite and Infinite Dimensional Systems, 261–84. Boston, MA: Springer US, 1998. http://dx.doi.org/10.1007/978-1-4615-5575-9_13.

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Desch, W., and W. Schappacher. "Linearized stability for nonlinear semigroups." In Lecture Notes in Mathematics, 61–73. Berlin, Heidelberg: Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/bfb0099183.

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Bhat, B. V. Rajarama, and Sachi Srivastava. "Stability of Quantum Dynamical Semigroups." In Operator Semigroups Meet Complex Analysis, Harmonic Analysis and Mathematical Physics, 67–85. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-18494-4_5.

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Del Moral, Pierre. "Stability of Feynman-Kac Semigroups." In Probability and its Applications, 121–55. New York, NY: Springer New York, 2004. http://dx.doi.org/10.1007/978-1-4684-9393-1_4.

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Belfakih, Keltouma, Elhoucien Elqorachi, and Themistocles M. Rassias. "Solutions and Stability of Some Functional Equations on Semigroups." In Ulam Type Stability, 167–98. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-28972-0_9.

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Eisner, Tanja. "Stability of linear operators." In Stability of Operators and Operator Semigroups, 37–77. Basel: Springer Basel, 2010. http://dx.doi.org/10.1007/978-3-0346-0195-5_2.

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Conference papers on the topic "Semigroup stability"

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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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Balas, Mark J., and Susan A. Frost. "A Stabilization of Fixed Gain Controlled Infinite Dimensional Systems by Augmentation With Direct Adaptive Control." In ASME 2017 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/smasis2017-3726.

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Linear infinite dimensional systems are described by a closed, densely defined linear operator that generates a continuous semigroup of bounded operators on a general Hilbert space of states and are controlled via a finite number of actuators and sensors. Many distributed applications are included in this formulation, such as large flexible aerospace structures, adaptive optics, diffusion reactions, smart electric power grids, and quantum information systems. We have developed the following stability result: an infinite dimensional linear system is Almost Strictly Dissipative (ASD) if and only if its high frequency gain CB is symmetric and positive definite and the open loop system is minimum phase, i.e. its transmission zeros are all exponentially stable. In this paper, we focus on infinite dimensional linear systems for which a fixed gain linear infinite or finite dimensional controller is already in place. It is usually true that fixed gain controllers are designed for particular applications but these controllers may not be able to stabilize the plant under all variations in the operating domain. Therefore we propose to augment this fixed gain controller with a relatively simple direct adaptive controller that will maintain stability of the full closed loop system over a much larger domain of operation. This can ensure that a flexible structure controller based on a reduced order model will still maintain closed-loop stability in the presence of unmodeled system dynamics. The augmentation approach is also valuable to reduce risk in loss of control situations. First we show that the transmission zeros of the augmented infinite dimensional system are the open loop plant transmission zeros and the eigenvalues (or poles) of the fixed gain controller. So when the open-loop plant transmission zeros are exponentially stable, the addition of any stable fixed gain controller does not alter the stability of the transmission zeros. Therefore the combined plant plus controller is ASD and the closed loop stability when the direct adaptive controller augments this combined system is retained. Consequently direct adaptive augmentation of controlled linear infinite dimensional systems can produce robust stabilization even when the fixed gain controller is based on approximation of the original system. These results are illustrated by application to a general infinite dimensional model described by nuclear operators with compact resolvent which are representative of distributed parameter models of mechanically flexible structures. with a reduced order model based controller and adaptive augmentation.
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Balas, Mark J. "Augmentation of Fixed Gain Controlled Infinite Dimensional Systems With Direct Adaptive Control." In ASME 2020 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/imece2020-23179.

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Abstract Linear infinite dimensional systems are described by a closed, densely defined linear operator that generates a continuous semigroup of bounded operators on a general Hilbert space of states and are controlled via a finite number of actuators and sensors. Many distributed applications are included in this formulation, such as large flexible aerospace structures, adaptive optics, diffusion reactions, smart electric power grids, and quantum information systems. In this paper, we focus on infinite dimensional linear systems for which a fixed gain linear infinite or finite dimensional controller is already in place. We augment this controller with a direct adaptive controller that will maintain stability of the full closed loop system even when the fixed gain controller fails to do so. We prove that the transmission zeros of the combined system are the original open loop transmission zeros, and the point spectrum of the controller alone. Therefore, the combined plant plus controller is Almost Strictly Dissipative (ASD) if and only if the original open loop system is minimum phase, and the fixed gain controller alone is exponentially stable. This result is true whether the fixed gain controller is finite or infinite dimensional. In particular this guarantees that a controller for an infinite dimensional plant based on a reduced -order approximation can be stabilized by augmentation with direct adaptive control to mitigate risks. These results are illustrated by application to direct adaptive control of general linear diffusion systems on a Hilbert space that are described by self-adjoint operators with compact resolvent.
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Chill, Ralph, and Yuri Tomilov. "Stability of operator semigroups: ideas and results." In Perspectives in Operator Theory. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2007. http://dx.doi.org/10.4064/bc75-0-6.

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Balas, Mark J., and Susan A. Frost. "Adaptive Tracking Control for Linear Infinite Dimensional Systems." In ASME 2016 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/smasis2016-9098.

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Tracking an ensemble of basic signals is often required of control systems in general. Here we are given a linear continuous-time infinite-dimensional plant on a Hilbert space and a space of tracking signals generated by a finite basis, and we show that there exists a stabilizing direct adaptive control law that will stabilize the plant and cause it to asymptotically track any member of this collection of signals. The plant is described by a closed, densely defined linear operator that generates a continuous semigroup of bounded operators on the Hilbert space of states. There is no state or parameter estimation used in this adaptive approach. Our results are illustrated by adaptive control of general linear diffusion systems.
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