C0 Semigroup Methods For Delay Equations

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C0-Semigroup Methods for Delay Equations

Author :
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (652 download)

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Book Synopsis C0-Semigroup Methods for Delay Equations by :

Download or read book C0-Semigroup Methods for Delay Equations written by and published by . This book was released on 2008 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In the dissertation tools for the analysis of well-posedness and asymptotic behaviour of integro-differential equations and delay equations are developed. In the first part (chapter 1 and 2) methods for the determination of the modulus semigroup (smallest dominating C0-semigroup) of a C0-semigroup are provided and applied to various examples such as Volterra semigroups and evolution semigroups and transport evolution equations in networks. The main interest of the second part (chapter 3 and 4) is a type of an integro-differential equation which occurs in the modelling of the flutter of airfoils at subsonic speed. The remarkable property of the equation is the time derivative of the sought function in the integral term. A number of well-posedness criteria are proved for which integration by parts is not possible. The developed methods are also suitable for the derivation of new well-posedness results for other delay semigroups. Corresponding criteria are presented in chapter 4.

C0-Semigroup Methods for Delay Equations

Author : Martin Stein
Publisher :
ISBN 13 :
Total Pages : 260 pages
Book Rating : 4.:/5 (316 download)

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Book Synopsis C0-Semigroup Methods for Delay Equations by : Martin Stein

Download or read book C0-Semigroup Methods for Delay Equations written by Martin Stein and published by . This book was released on 2007 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt:

C_1tn0-semigroup Methods for Delay Equations

Author : Martin Stein
Publisher :
ISBN 13 :
Total Pages : 260 pages
Book Rating : 4.:/5 (724 download)

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Book Synopsis C_1tn0-semigroup Methods for Delay Equations by : Martin Stein

Download or read book C_1tn0-semigroup Methods for Delay Equations written by Martin Stein and published by . This book was released on 2007 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Semigroups for Delay Equations

Author : András Bátkai
Publisher : A K Peters, Ltd.
ISBN 13 : 9781568812434
Total Pages : 259 pages
Book Rating : 4.8/5 (124 download)

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Book Synopsis Semigroups for Delay Equations by : András Bátkai

Download or read book Semigroups for Delay Equations written by András Bátkai and published by A K Peters, Ltd.. This book was released on 2005 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: In most physical, chemical, biological and economic phenomena it is quite natural to assume that the system not only depends on the present state but also on past occurrences. These circumstances are mathematically described by partial differential equations with delay. This book presents, in a systematic fashion, how delay equations can be studied in Lp-history spaces.Appendices offering supplementary information and a comprehensive index make this book an ideal introduction and research tool for mathematicians, chemists, biologists and economists.

Delay Equations

Author : Odo Diekmann
Publisher : Springer Science & Business Media
ISBN 13 : 1461242061
Total Pages : 547 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Delay Equations by : Odo Diekmann

Download or read book Delay Equations written by Odo Diekmann and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 547 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim here is to provide an introduction to the mathematical theory of infinite dimensional dynamical systems by focusing on a relatively simple - yet rich - class of examples, delay differential equations. This textbook contains detailed proofs and many exercises, intended both for self-study and for courses at graduate level, as well as a reference for basic results. As the subtitle indicates, this book is about concepts, ideas, results and methods from linear functional analysis, complex function theory, the qualitative theory of dynamical systems and nonlinear analysis. The book provides the reader with a working knowledge of applied functional analysis and dynamical systems.

Theory and Applications of Abstract Semilinear Cauchy Problems

Author : Pierre Magal
Publisher : Springer
ISBN 13 : 3030015068
Total Pages : 543 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Theory and Applications of Abstract Semilinear Cauchy Problems by : Pierre Magal

Download or read book Theory and Applications of Abstract Semilinear Cauchy Problems written by Pierre Magal and published by Springer. This book was released on 2018-11-21 with total page 543 pages. Available in PDF, EPUB and Kindle. Book excerpt: Several types of differential equations, such as functional differential equation, age-structured models, transport equations, reaction-diffusion equations, and partial differential equations with delay, can be formulated as abstract Cauchy problems with non-dense domain. This monograph provides a self-contained and comprehensive presentation of the fundamental theory of non-densely defined semilinear Cauchy problems and their applications. Starting from the classical Hille-Yosida theorem, semigroup method, and spectral theory, this monograph introduces the abstract Cauchy problems with non-dense domain, integrated semigroups, the existence of integrated solutions, positivity of solutions, Lipschitz perturbation, differentiability of solutions with respect to the state variable, and time differentiability of solutions. Combining the functional analysis method and bifurcation approach in dynamical systems, then the nonlinear dynamics such as the stability of equilibria, center manifold theory, Hopf bifurcation, and normal form theory are established for abstract Cauchy problems with non-dense domain. Finally applications to functional differential equations, age-structured models, and parabolic equations are presented. This monograph will be very valuable for graduate students and researchers in the fields of abstract Cauchy problems, infinite dimensional dynamical systems, and their applications in biological, chemical, medical, and physical problems.

Semigroups for Delay Equations

Author : Andras Batkai
Publisher : CRC Press
ISBN 13 : 143986568X
Total Pages : 272 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis Semigroups for Delay Equations by : Andras Batkai

Download or read book Semigroups for Delay Equations written by Andras Batkai and published by CRC Press. This book was released on 2005-09-05 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: In most physical, chemical, biological and economic phenomena it is quite natural to assume that the system not only depends on the present state but also on past occurrences. These circumstances are mathematically described by partial differential equations with delay. This book presents, in a systematic fashion, how delay equations can be studied

Semigroup Methods for Evolution Equations on Networks

Author : Delio Mugnolo
Publisher : Springer
ISBN 13 : 3319046217
Total Pages : 294 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Semigroup Methods for Evolution Equations on Networks by : Delio Mugnolo

Download or read book Semigroup Methods for Evolution Equations on Networks written by Delio Mugnolo and published by Springer. This book was released on 2014-05-21 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: This concise text is based on a series of lectures held only a few years ago and originally intended as an introduction to known results on linear hyperbolic and parabolic equations. Yet the topic of differential equations on graphs, ramified spaces, and more general network-like objects has recently gained significant momentum and, well beyond the confines of mathematics, there is a lively interdisciplinary discourse on all aspects of so-called complex networks. Such network-like structures can be found in virtually all branches of science, engineering and the humanities, and future research thus calls for solid theoretical foundations. This book is specifically devoted to the study of evolution equations – i.e., of time-dependent differential equations such as the heat equation, the wave equation, or the Schrödinger equation (quantum graphs) – bearing in mind that the majority of the literature in the last ten years on the subject of differential equations of graphs has been devoted to elliptic equations and related spectral problems. Moreover, for tackling the most general settings - e.g. encoded in the transmission conditions in the network nodes - one classical and elegant tool is that of operator semigroups. This book is simultaneously a very concise introduction to this theory and a handbook on its applications to differential equations on networks. With a more interdisciplinary readership in mind, full proofs of mathematical statements have been frequently omitted in favor of keeping the text as concise, fluid and self-contained as possible. In addition, a brief chapter devoted to the field of neurodynamics of the brain cortex provides a concrete link to ongoing applied research.

Numerical Methods for Delay Differential Equations

Author : Alfredo Bellen
Publisher : OUP Oxford
ISBN 13 : 0191523135
Total Pages : 410 pages
Book Rating : 4.1/5 (915 download)

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Book Synopsis Numerical Methods for Delay Differential Equations by : Alfredo Bellen

Download or read book Numerical Methods for Delay Differential Equations written by Alfredo Bellen and published by OUP Oxford. This book was released on 2003-03-20 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main purpose of the book is to introduce the readers to the numerical integration of the Cauchy problem for delay differential equations (DDEs). Peculiarities and differences that DDEs exhibit with respect to ordinary differential equations are preliminarily outlined by numerous examples illustrating some unexpected, and often surprising, behaviours of the analytical and numerical solutions. The effect of various kinds of delays on the regularity of the solution is described and some essential existence and uniqueness results are reported. The book is centered on the use of Runge-Kutta methods continuously extended by polynomial interpolation, includes a brief review of the various approaches existing in the literature, and develops an exhaustive error and well-posedness analysis for the general classes of one-step and multistep methods. The book presents a comprehensive development of continuous extensions of Runge-Kutta methods which are of interest also in the numerical treatment of more general problems such as dense output, discontinuous equations, etc. Some deeper insight into convergence and superconvergence of continuous Runge-Kutta methods is carried out for DDEs with various kinds of delays. The stepsize control mechanism is also developed on a firm mathematical basis relying on the discrete and continuous local error estimates. Classical results and a unconventional analysis of "stability with respect to forcing term" is reviewed for ordinary differential equations in view of the subsequent numerical stability analysis. Moreover, an exhaustive description of stability domains for some test DDEs is carried out and the corresponding stability requirements for the numerical methods are assessed and investigated. Alternative approaches, based on suitable formulation of DDEs as partial differential equations and subsequent semidiscretization are briefly described and compared with the classical approach. A list of available codes is provided, and illustrative examples, pseudo-codes and numerical experiments are included throughout the book.

Numerical Methods for Delay Differential Equations

Author : Alfredo Bellen
Publisher : Numerical Mathematics and Scie
ISBN 13 : 0199671370
Total Pages : 411 pages
Book Rating : 4.1/5 (996 download)

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Book Synopsis Numerical Methods for Delay Differential Equations by : Alfredo Bellen

Download or read book Numerical Methods for Delay Differential Equations written by Alfredo Bellen and published by Numerical Mathematics and Scie. This book was released on 2013-01-10 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique book describes, analyses, and improves various approaches and techniques for the numerical solution of delay differential equations. It includes a list of available codes and also aids the reader in writing his or her own.

One-Parameter Semigroups for Linear Evolution Equations

Author : Klaus-Jochen Engel
Publisher : Springer Science & Business Media
ISBN 13 : 0387226427
Total Pages : 609 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis One-Parameter Semigroups for Linear Evolution Equations by : Klaus-Jochen Engel

Download or read book One-Parameter Semigroups for Linear Evolution Equations written by Klaus-Jochen Engel and published by Springer Science & Business Media. This book was released on 2006-04-06 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the theory of strongly continuous one-parameter semigroups of linear operators. A special feature of the text is an unusually wide range of applications such as to ordinary and partial differential operators, to delay and Volterra equations, and to control theory. Also, the book places an emphasis on philosophical motivation and the historical background.

Stability of Linear Delay Differential Equations

Author : Dimitri Breda
Publisher : Springer
ISBN 13 : 149392107X
Total Pages : 162 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis Stability of Linear Delay Differential Equations by : Dimitri Breda

Download or read book Stability of Linear Delay Differential Equations written by Dimitri Breda and published by Springer. This book was released on 2014-10-21 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the authors' recent work on the numerical methods for the stability analysis of linear autonomous and periodic delay differential equations, which consist in applying pseudospectral techniques to discretize either the solution operator or the infinitesimal generator and in using the eigenvalues of the resulting matrices to approximate the exact spectra. The purpose of the book is to provide a complete and self-contained treatment, which includes the basic underlying mathematics and numerics, examples from population dynamics and engineering applications, and Matlab programs implementing the proposed numerical methods. A number of proofs is given to furnish a solid foundation, but the emphasis is on the (unifying) idea of the pseudospectral technique for the stability analysis of DDEs. It is aimed at advanced students and researchers in applied mathematics, in dynamical systems and in various fields of science and engineering, concerned with delay systems. A relevant feature of the book is that it also provides the Matlab codes to encourage the readers to experience the practical aspects. They could use the codes to test the theory and to analyze the performances of the methods on the given examples. Moreover, they could easily modify them to tackle the numerical stability analysis of their own delay models.

Stabilization of Distributed Parameter Systems: Design Methods and Applications

Author : Grigory Sklyar
Publisher : Springer Nature
ISBN 13 : 3030617424
Total Pages : 139 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Stabilization of Distributed Parameter Systems: Design Methods and Applications by : Grigory Sklyar

Download or read book Stabilization of Distributed Parameter Systems: Design Methods and Applications written by Grigory Sklyar and published by Springer Nature. This book was released on 2021-03-01 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents recent results and envisages new solutions of the stabilization problem for infinite-dimensional control systems. Its content is based on the extended versions of presentations at the Thematic Minisymposium “Stabilization of Distributed Parameter Systems: Design Methods and Applications” at ICIAM 2019, held in Valencia from 15 to 19 July 2019. This volume aims at bringing together contributions on stabilizing control design for different classes of dynamical systems described by partial differential equations, functional-differential equations, delay equations, and dynamical systems in abstract spaces. This includes new results in the theory of nonlinear semigroups, port-Hamiltonian systems, turnpike phenomenon, and further developments of Lyapunov's direct method. The scope of the book also covers applications of these methods to mathematical models in continuum mechanics and chemical engineering. It is addressed to readers interested in control theory, differential equations, and dynamical systems.

Analysis and Synthesis of Time Delay Systems

Author : Henryk Gorecki
Publisher :
ISBN 13 :
Total Pages : 392 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Analysis and Synthesis of Time Delay Systems by : Henryk Gorecki

Download or read book Analysis and Synthesis of Time Delay Systems written by Henryk Gorecki and published by . This book was released on 1989-10-27 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a comprehensive review of the modern theory of control systems described by functional-differential equations. The emphasis of the text is on methods and results that are applicable to analysis and synthesis of industrial control systems with time delays. Initial chapters contain examples of systems with delays and a presentation of typical control problems. Chapters also present basic results of the mathematical theory of functional-differential and discrete equations and cover identification of time-delay systems, stability theory, PID and Smith controllers, as well as the determination of stability regions, controller settings, and more. A review of controlability and observability results is presented, and optimal control is discussed in detail.

Topological Methods for Delay and Ordinary Differential Equations

Author : Pablo Amster
Publisher : Springer Nature
ISBN 13 : 3031613376
Total Pages : 220 pages
Book Rating : 4.0/5 (316 download)

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Book Synopsis Topological Methods for Delay and Ordinary Differential Equations by : Pablo Amster

Download or read book Topological Methods for Delay and Ordinary Differential Equations written by Pablo Amster and published by Springer Nature. This book was released on with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Evolution Equations

Author : Gisele Ruiz Goldstein
Publisher : CRC Press
ISBN 13 : 9780824709754
Total Pages : 442 pages
Book Rating : 4.7/5 (97 download)

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Book Synopsis Evolution Equations by : Gisele Ruiz Goldstein

Download or read book Evolution Equations written by Gisele Ruiz Goldstein and published by CRC Press. This book was released on 2003-06-24 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: Celebrating the work of renowned mathematician Jerome A. Goldstein, this reference compiles original research on the theory and application of evolution equations to stochastics, physics, engineering, biology, and finance. The text explores a wide range of topics in linear and nonlinear semigroup theory, operator theory, functional analysis, and linear and nonlinear partial differential equations, and studies the latest theoretical developments and uses of evolution equations in a variety of disciplines. Providing nearly 500 references, the book contains discussions by renowned mathematicians such as H. Brezis, G. Da Prato, N.E. Gretskij, I. Lasiecka, Peter Lax, M. M. Rao, and R. Triggiani.

Evolution Equations and Approximations

Author : Kazufumi Ito
Publisher : World Scientific
ISBN 13 : 9789812380265
Total Pages : 524 pages
Book Rating : 4.3/5 (82 download)

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Book Synopsis Evolution Equations and Approximations by : Kazufumi Ito

Download or read book Evolution Equations and Approximations written by Kazufumi Ito and published by World Scientific. This book was released on 2002 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: Annotation Ito (North Carolina State U.) and Kappel (U. of Graz, Austria) offer a unified presentation of the general approach for well-posedness results using abstract evolution equations, drawing from and modifying the work of K. and Y. Kobayashi and S. Oharu. They also explore abstract approximation results for evolution equations. Their work is not a textbook, but they explain how instructors can use various sections, or combinations of them, as a foundation for a range of courses. Annotation copyrighted by Book News, Inc., Portland, OR