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Languages : en
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Book Description
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.
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages :
Get Book Here
Book Description
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.
Author: Martin Stein
Publisher:
ISBN:
Category :
Languages : en
Pages : 260
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Book Description
Author: Martin Stein
Publisher:
ISBN:
Category :
Languages : en
Pages : 260
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Book Description
Author: András Bátkai
Publisher: A K Peters, Ltd.
ISBN: 9781568812434
Category : Mathematics
Languages : en
Pages : 259
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Book Description
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.
Author: Dimitri Breda
Publisher: Springer
ISBN: 149392107X
Category : Science
Languages : en
Pages : 162
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Book Description
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.
Author: Andras Batkai
Publisher: CRC Press
ISBN: 143986568X
Category : Mathematics
Languages : en
Pages : 272
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Book Description
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
Author: Odo Diekmann
Publisher: Springer Science & Business Media
ISBN: 1461242061
Category : Mathematics
Languages : en
Pages : 547
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Book Description
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.
Author: Pierre Magal
Publisher: Springer
ISBN: 3030015068
Category : Mathematics
Languages : en
Pages : 558
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Book Description
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.
Author: Alfredo Bellen
Publisher: Numerical Mathematics and Scie
ISBN: 0199671370
Category : Business & Economics
Languages : en
Pages : 411
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Book Description
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.
Author: Delio Mugnolo
Publisher: Springer
ISBN: 3319046217
Category : Science
Languages : en
Pages : 294
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Book Description
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.
