An Introduction To Semiflows

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An Introduction to Semiflows

Author : Albert J. Milani
Publisher : CRC Press
ISBN 13 : 9780367454289
Total Pages : 386 pages
Book Rating : 4.4/5 (542 download)

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Book Synopsis An Introduction to Semiflows by : Albert J. Milani

Download or read book An Introduction to Semiflows written by Albert J. Milani and published by CRC Press. This book was released on 2019-11-25 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the class of dynamical systems called semiflows, which includes systems defined or modeled by certain types of differential evolution equations (DEEs). It focuses on the basic results of the theory of dynamical systems that can be extended naturally and applied to study the asymptotic behavior of the solutions of DEEs. The authors concentrate on three types of absorbing sets: attractors, exponential attractors, and inertial manifolds. They present the fundamental properties of these sets, and then proceed to show the existence of some of these sets for a number of dynamical systems generated by well-known physical models. In particular, they consider in full detail two particular PDEEs: a semilinear version of the heat equation and a corresponding version of the dissipative wave equation. These examples illustrate the most important features of the theory of semiflows and provide a sort of template that can be applied to the analysis of other models. The material builds in a careful, gradual progression, developing the background needed by newcomers to the field, and culminating in a more detailed presentation of the main topics than found in most sources. The authors' approach to and treatment of the subject builds the foundation for more advanced references and research on global attractors, exponential attractors, and inertial manifolds.

An Introduction to Semiflows

Author : Albert J. Milani
Publisher : CRC Press
ISBN 13 : 1000738221
Total Pages : 286 pages
Book Rating : 4.0/5 (7 download)

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Book Synopsis An Introduction to Semiflows by : Albert J. Milani

Download or read book An Introduction to Semiflows written by Albert J. Milani and published by CRC Press. This book was released on 2004-10-14 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the class of dynamical systems called semiflows, which includes systems defined or modeled by certain types of differential evolution equations (DEEs). It focuses on the basic results of the theory of dynamical systems that can be extended naturally and applied to study the asymptotic behavior of the solutions of DEEs. The auth

Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems

Author : Hal L. Smith
Publisher : American Mathematical Soc.
ISBN 13 : 0821844873
Total Pages : 186 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems by : Hal L. Smith

Download or read book Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems written by Hal L. Smith and published by American Mathematical Soc.. This book was released on 1995 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents comprehensive treatment of a rapidly developing area with many potential applications: the theory of monotone dynamical systems and the theory of competitive and cooperative differential equations. The primary aim is to provide potential users of the theory with techniques, results, and ideas useful in applications, while at the same time providing rigorous proofs. Among the topics discussed in the book are continuous-time monotone dynamical systems, and quasimonotone and nonquasimonotone delay differential equations. The book closes with a discussion of applications to quasimonotone systems of reaction-diffusion type. Throughout the book, applications of the theory to many mathematical models arising in biology are discussed. Requiring a background in dynamical systems at the level of a first graduate course, this book is useful to graduate students and researchers working in the theory of dynamical systems and its applications.

Almost Automorphic and Almost Periodic Dynamics in Skew-Product Semiflows

Author : Wenxian Shen
Publisher : American Mathematical Soc.
ISBN 13 : 0821808672
Total Pages : 111 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Almost Automorphic and Almost Periodic Dynamics in Skew-Product Semiflows by : Wenxian Shen

Download or read book Almost Automorphic and Almost Periodic Dynamics in Skew-Product Semiflows written by Wenxian Shen and published by American Mathematical Soc.. This book was released on 1998 with total page 111 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is devoted to the study of almost automorphic dynamics in differential equations. By making use of techniques from abstract topological dynamics, it is shown that almost automorphy, a notion which was introduced by S. Bochner in 1955, is essential and fundamental in the qualitative study of almost periodic differential equations.

Dynamical Systems in Population Biology

Author : Xiao-Qiang Zhao
Publisher : Springer
ISBN 13 : 3319564331
Total Pages : 413 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Dynamical Systems in Population Biology by : Xiao-Qiang Zhao

Download or read book Dynamical Systems in Population Biology written by Xiao-Qiang Zhao and published by Springer. This book was released on 2017-04-11 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: This research monograph provides an introduction to the theory of nonautonomous semiflows with applications to population dynamics. It develops dynamical system approaches to various evolutionary equations such as difference, ordinary, functional, and partial differential equations, and pays more attention to periodic and almost periodic phenomena. The presentation includes persistence theory, monotone dynamics, periodic and almost periodic semiflows, basic reproduction ratios, traveling waves, and global analysis of prototypical population models in ecology and epidemiology. Research mathematicians working with nonlinear dynamics, particularly those interested in applications to biology, will find this book useful. It may also be used as a textbook or as supplementary reading for a graduate special topics course on the theory and applications of dynamical systems. Dr. Xiao-Qiang Zhao is a University Research Professor at Memorial University of Newfoundland, Canada. His main research interests involve applied dynamical systems, nonlinear differential equations, and mathematical biology. He is the author of more than 100 papers, and his research has played an important role in the development of the theory and applications of monotone dynamical systems, periodic and almost periodic semiflows, uniform persistence, and basic reproduction ratios.

Formal Techniques for Distributed Objects, Components, and Systems

Author : Marieke Huisman
Publisher : Springer Nature
ISBN 13 : 3031353552
Total Pages : 233 pages
Book Rating : 4.0/5 (313 download)

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Book Synopsis Formal Techniques for Distributed Objects, Components, and Systems by : Marieke Huisman

Download or read book Formal Techniques for Distributed Objects, Components, and Systems written by Marieke Huisman and published by Springer Nature. This book was released on 2023-06-09 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 43rd IFIP WG 6.1 International Conference on Formal Techniques for Distributed Objects, Components, and Systems, FORTE 2023, held in Lisbon, Portugal, in June 2023, as part of the 18th International Federated Conference on Distributed Computing Techniques, DisCoTec 2023. The 13 regular papers and 3 short papers presented in this book were carefully reviewed and selected from 26 submissions. They cover topics such as: concurrent programming; security; probabilities, time and other resources; and model-based testing and petri nets.

Semigroups of Operators – Theory and Applications

Author : Jacek Banasiak
Publisher : Springer Nature
ISBN 13 : 3030460797
Total Pages : 446 pages
Book Rating : 4.0/5 (34 download)

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Book Synopsis Semigroups of Operators – Theory and Applications by : Jacek Banasiak

Download or read book Semigroups of Operators – Theory and Applications written by Jacek Banasiak and published by Springer Nature. This book was released on 2020-06-12 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book features selected and peer-reviewed lectures presented at the 3rd Semigroups of Operators: Theory and Applications Conference, held in Kazimierz Dolny, Poland, in October 2018 to mark the 85th birthday of Jan Kisyński. Held every five years, the conference offers a forum for mathematicians using semigroup theory to discover what is happening outside their particular field of research and helps establish new links between various sub-disciplines of semigroup theory, stochastic processes, differential equations and the applied fields. The book is intended for researchers, postgraduate and senior students working in operator theory, partial differential equations, probability and stochastic processes, analytical methods in biology and other natural sciences, optimisation and optimal control. The theory of semigroups of operators is a well-developed branch of functional analysis. Its foundations were laid at the beginning of the 20th century, while Hille and Yosida’s fundamental generation theorem dates back to the forties. The theory was originally designed as a universal language for partial differential equations and stochastic processes but, at the same time, it started to become an independent branch of operator theory. Today, it still has the same distinctive character: it develops rapidly by posing new ‘internal’ questions and, in answering them, discovering new methods that can be used in applications. On the other hand, it is being influenced by questions from PDE’s and stochastic processes as well as from applied sciences such as mathematical biology and optimal control and, as a result, it continually gathers new momentum. However, many results, both from semigroup theory itself and the applied sciences, are phrased in discipline-specific languages and are hardly known to the broader community.

Geometric Theory of Discrete Nonautonomous Dynamical Systems

Author : Christian Pötzsche
Publisher : Springer
ISBN 13 : 3642142583
Total Pages : 422 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Geometric Theory of Discrete Nonautonomous Dynamical Systems by : Christian Pötzsche

Download or read book Geometric Theory of Discrete Nonautonomous Dynamical Systems written by Christian Pötzsche and published by Springer. This book was released on 2010-08-24 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonautonomous dynamical systems provide a mathematical framework for temporally changing phenomena, where the law of evolution varies in time due to seasonal, modulation, controlling or even random effects. Our goal is to provide an approach to the corresponding geometric theory of nonautonomous discrete dynamical systems in infinite-dimensional spaces by virtue of 2-parameter semigroups (processes). These dynamical systems are generated by implicit difference equations, which explicitly depend on time. Compactness and dissipativity conditions are provided for such problems in order to have attractors using the natural concept of pullback convergence. Concerning a necessary linear theory, our hyperbolicity concept is based on exponential dichotomies and splittings. This concept is in turn used to construct nonautonomous invariant manifolds, so-called fiber bundles, and deduce linearization theorems. The results are illustrated using temporal and full discretizations of evolutionary differential equations.

Ordinary Differential Equations

Author : Herbert Amann
Publisher : Walter de Gruyter
ISBN 13 : 3110853698
Total Pages : 473 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis Ordinary Differential Equations by : Herbert Amann

Download or read book Ordinary Differential Equations written by Herbert Amann and published by Walter de Gruyter. This book was released on 2011-04-20 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 30 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob.

Navier–Stokes Equations

Author : Grzegorz Łukaszewicz
Publisher : Springer
ISBN 13 : 331927760X
Total Pages : 390 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Navier–Stokes Equations by : Grzegorz Łukaszewicz

Download or read book Navier–Stokes Equations written by Grzegorz Łukaszewicz and published by Springer. This book was released on 2016-04-12 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is devoted to the study of the Navier–Stokes equations, providing a comprehensive reference for a range of applications: from advanced undergraduate students to engineers and professional mathematicians involved in research on fluid mechanics, dynamical systems, and mathematical modeling. Equipped with only a basic knowledge of calculus, functional analysis, and partial differential equations, the reader is introduced to the concept and applications of the Navier–Stokes equations through a series of fully self-contained chapters. Including lively illustrations that complement and elucidate the text, and a collection of exercises at the end of each chapter, this book is an indispensable, accessible, classroom-tested tool for teaching and understanding the Navier–Stokes equations. Incompressible Navier–Stokes equations describe the dynamic motion (flow) of incompressible fluid, the unknowns being the velocity and pressure as functions of location (space) and time variables. A solution to these equations predicts the behavior of the fluid, assuming knowledge of its initial and boundary states. These equations are one of the most important models of mathematical physics: although they have been a subject of vivid research for more than 150 years, there are still many open problems due to the nature of nonlinearity present in the equations. The nonlinear convective term present in the equations leads to phenomena such as eddy flows and turbulence. In particular, the question of solution regularity for three-dimensional problem was appointed by Clay Institute as one of the Millennium Problems, the key problems in modern mathematics. The problem remains challenging and fascinating for mathematicians, and the applications of the Navier–Stokes equations range from aerodynamics (drag and lift forces), to the design of watercraft and hydroelectric power plants, to medical applications such as modeling the flow of blood in the circulatory system.

Handbook of Differential Equations: Ordinary Differential Equations

Author : A. Canada
Publisher : Elsevier
ISBN 13 : 0080532829
Total Pages : 709 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Handbook of Differential Equations: Ordinary Differential Equations by : A. Canada

Download or read book Handbook of Differential Equations: Ordinary Differential Equations written by A. Canada and published by Elsevier. This book was released on 2004-09-09 with total page 709 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book contains seven survey papers about ordinary differential equations.The common feature of all papers consists in the fact that nonlinear equations are focused on. This reflects the situation in modern mathematical modelling - nonlinear mathematical models are more realistic and describe the real world problems more accurately. The implications are that new methods and approaches have to be looked for, developed and adopted in order to understand and solve nonlinear ordinary differential equations.The purpose of this volume is to inform the mathematical community and also other scientists interested in and using the mathematical apparatus of ordinary differential equations, about some of these methods and possible applications.

Semiflows on Topological Spaces

Author : Mauro Patrão
Publisher :
ISBN 13 :
Total Pages : 42 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Semiflows on Topological Spaces by : Mauro Patrão

Download or read book Semiflows on Topological Spaces written by Mauro Patrão and published by . This book was released on 2005 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Infinite-Dimensional Dynamical Systems

Author : James C. Robinson
Publisher : Cambridge University Press
ISBN 13 : 9780521632041
Total Pages : 488 pages
Book Rating : 4.6/5 (32 download)

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Book Synopsis Infinite-Dimensional Dynamical Systems by : James C. Robinson

Download or read book Infinite-Dimensional Dynamical Systems written by James C. Robinson and published by Cambridge University Press. This book was released on 2001-04-23 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book treats the theory of global attractors, a recent development in the theory of partial differential equations, in a way that also includes much of the traditional elements of the subject. As such it gives a quick but directed introduction to some fundamental concepts, and by the end proceeds to current research problems. Since the subject is relatively new, this is the first book to attempt to treat these various topics in a unified and didactic way. It is intended to be suitable for first year graduate students.

Topological Dynamics and Applications

Author : Robert Ellis
Publisher : American Mathematical Soc.
ISBN 13 : 0821806084
Total Pages : 348 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Topological Dynamics and Applications by : Robert Ellis

Download or read book Topological Dynamics and Applications written by Robert Ellis and published by American Mathematical Soc.. This book was released on 1998 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a very readable exposition of the modern theory of topological dynamics and presents diverse applications to such areas as ergodic theory, combinatorial number theory and differential equations. There are three parts: 1) The abstract theory of topological dynamics is discussed, including a comprehensive survey by Furstenberg and Glasner on the work and influence of R. Ellis. Presented in book form for the first time are new topics in the theory of dynamical systems, such as weak almost-periodicity, hidden eigenvalues, a natural family of factors and topological analogues of ergodic decomposition. 2) The power of abstract techniques is demonstrated by giving a very wide range of applications to areas of ergodic theory, combinatorial number theory, random walks on groups and others. 3) Applications to non-autonomous linear differential equations are shown. Exposition on recent results about Floquet theory, bifurcation theory and Lyapanov exponents is given.

Tools and Algorithms for the Construction and Analysis of Systems

Author : Tiziana Margaria
Publisher : Springer
ISBN 13 : 3540453199
Total Pages : 602 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Tools and Algorithms for the Construction and Analysis of Systems by : Tiziana Margaria

Download or read book Tools and Algorithms for the Construction and Analysis of Systems written by Tiziana Margaria and published by Springer. This book was released on 2003-06-29 with total page 602 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 7th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2001. The 36 revised full papers presented together with an invited contribution were carefully reviewed and selected from a total of 125 submissions. The papers are organized in sections on symbolic verification, infinite state systems - deduction and abstraction, application of model checking techniques, timed and probabilistic systems, hardware - design and verification, software verification, testing - techniques and tools, implementation techniques, semantics and compositional verification, logics and model checking, and ETAPS tool demonstration.

Dynamics of Infinite Dimensional Systems

Author : Shui-Nee Chow
Publisher : Springer Science & Business Media
ISBN 13 : 3642864589
Total Pages : 509 pages
Book Rating : 4.6/5 (428 download)

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Book Synopsis Dynamics of Infinite Dimensional Systems by : Shui-Nee Chow

Download or read book Dynamics of Infinite Dimensional Systems written by Shui-Nee Chow and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 509 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 1986 NATO Advanced Study Insti tute on Dynamics of Infini te Dimensional Systems was held at the Instituto Superior Tecnico. Lisbon. Portugal. In recent years. there have been several research workers who have been considering partial differential equations and functional differential equations as dynamical systems on function spaces. Such approaches have led to the formulation of more theoretical problems that need to be investigated. In the applications. the theoretical ideas have contributed significantly to a better understanding of phenomena that have been experimentally and computationally observed. The investigators of this development come wi th several different backgrounds - some from classical partial differential equations. some from classical ordinary differential equations and some interested in specific applications. Each group has special ideas and often these ideas have not been transmitted from one group to another. The purpose of this NATO Workshop was to bring together research workers from these various areas. It provided asoundboard for the impact of the ideas of each respective discipline. We believe that goal was accomplished. but time will be a better judge. We have included the list of participants at the workshop. with most of these giving a presentation. Although the proceedings do not include all of the presentations. it is a good representative sampie. We wish to express our gratitude to NATO. and.to Dr. M. di Lullo of NATO. who unfortunately did not live to see the completion of this project.

Dynamical Systems

Author : Luis Barreira
Publisher : Springer Science & Business Media
ISBN 13 : 1447148355
Total Pages : 214 pages
Book Rating : 4.4/5 (471 download)

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Book Synopsis Dynamical Systems by : Luis Barreira

Download or read book Dynamical Systems written by Luis Barreira and published by Springer Science & Business Media. This book was released on 2012-12-02 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of dynamical systems is a broad and active research subject with connections to most parts of mathematics. Dynamical Systems: An Introduction undertakes the difficult task to provide a self-contained and compact introduction. Topics covered include topological, low-dimensional, hyperbolic and symbolic dynamics, as well as a brief introduction to ergodic theory. In particular, the authors consider topological recurrence, topological entropy, homeomorphisms and diffeomorphisms of the circle, Sharkovski's ordering, the Poincaré-Bendixson theory, and the construction of stable manifolds, as well as an introduction to geodesic flows and the study of hyperbolicity (the latter is often absent in a first introduction). Moreover, the authors introduce the basics of symbolic dynamics, the construction of symbolic codings, invariant measures, Poincaré's recurrence theorem and Birkhoff's ergodic theorem. The exposition is mathematically rigorous, concise and direct: all statements (except for some results from other areas) are proven. At the same time, the text illustrates the theory with many examples and 140 exercises of variable levels of difficulty. The only prerequisites are a background in linear algebra, analysis and elementary topology. This is a textbook primarily designed for a one-semester or two-semesters course at the advanced undergraduate or beginning graduate levels. It can also be used for self-study and as a starting point for more advanced topics.