The Asymptotic Behaviour Of Semigroups Of Linear Operators

Author : Jan van Neerven
Publisher : Birkhäuser
Page : 247 pages
File Size : 50,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034892063

Get Book

The Asymptotic Behaviour of Semigroups of Linear Operators by Jan van Neerven Pdf

This book presents a systematic account of the theory of asymptotic behaviour of semigroups of linear operators acting in a Banach space. The focus is on the relationship between asymptotic behaviour of the semigroup and spectral properties of its infinitesimal generator. The most recent developments in the field are included, such as the Arendt-Batty-Lyubich-Vu theorem, the spectral mapp- ing theorem of Latushkin and Montgomery-Smith, Weis's theorem on stability of positive semigroup in Lp-spaces, the stability theorem for semigroups whose resolvent is bounded in a half-plane, and a systematic theory of individual stability. Addressed to researchers and graduate students with interest in the fields of operator semigroups and evolution equations, this book is self-contained and provides complete proofs.

Author : Eduard Yu. Emel'yanov
Publisher : Springer Science & Business Media
Page : 181 pages
File Size : 53,6 Mb
Release : 2007-02-17
Category : Mathematics
ISBN : 9783764381141

Get Book

Non-spectral Asymptotic Analysis of One-Parameter Operator Semigroups by Eduard Yu. Emel'yanov Pdf

In this book, non-spectral methods are presented and discussed that have been developed over the last two decades for the investigation of asymptotic behavior of operator semigroups. This concerns in particular Markov semigroups in L1-spaces, motivated by applications to probability theory and dynamical systems. Related results, historical notes, exercises, and open problems accompany each chapter.

Author : Tanja Eisner
Publisher : Birkhäuser
Page : 208 pages
File Size : 54,6 Mb
Release : 2019-10-01
Category : Mathematics
ISBN : 9783034601955

Get Book

Stability of Operators and Operator Semigroups by Tanja Eisner Pdf

The asymptotic behaviour, in particular "stability" in some sense, is studied systematically for discrete and for continuous linear dynamical systems on Banach spaces. Of particular concern is convergence to an equilibrium with respect to various topologies. Parallels and differences between the discrete and the continuous situation are emphasised.

Author : Jerome A. Goldstein
Publisher : Courier Dover Publications
Page : 320 pages
File Size : 45,8 Mb
Release : 2017-05-17
Category : Mathematics
ISBN : 9780486822228

Get Book

Semigroups of Linear Operators and Applications by Jerome A. Goldstein Pdf

Advanced graduate-level treatment of semigroup theory explores semigroups of linear operators and linear Cauchy problems. The text features challenging exercises and emphasizes motivation, heuristics, and further applications. 1985 edition.

Author : A. C. McBride
Publisher : Longman Scientific and Technical
Page : 148 pages
File Size : 52,6 Mb
Release : 1987
Category : Linear operators
ISBN : UCAL:B4405484

Get Book

Semigroups of Linear Operators by A. C. McBride Pdf

Author : Klaus-Jochen Engel,Rainer Nagel
Publisher : Springer Science & Business Media
Page : 609 pages
File Size : 44,8 Mb
Release : 2006-04-06
Category : Mathematics
ISBN : 9780387226422

Get Book

One-Parameter Semigroups for Linear Evolution Equations by Klaus-Jochen Engel,Rainer Nagel Pdf

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.

Author : Shmuel Kantorovitz
Publisher : Springer Science & Business Media
Page : 266 pages
File Size : 41,5 Mb
Release : 2009-10-22
Category : Mathematics
ISBN : 9780817649326

Get Book

Topics in Operator Semigroups by Shmuel Kantorovitz Pdf

This monograph is concerned with the interplay between the theory of operator semigroups and spectral theory. The basics on operator semigroups are concisely covered in this self-contained text. Part I deals with the Hille--Yosida and Lumer--Phillips characterizations of semigroup generators, the Trotter--Kato approximation theorem, Kato’s unified treatment of the exponential formula and the Trotter product formula, the Hille--Phillips perturbation theorem, and Stone’s representation of unitary semigroups. Part II explores generalizations of spectral theory’s connection to operator semigroups.

Author : Klaus-Jochen Engel,Rainer Nagel
Publisher : Springer Science & Business Media
Page : 257 pages
File Size : 51,6 Mb
Release : 2006-06-06
Category : Mathematics
ISBN : 9780387313412

Get Book

A Short Course on Operator Semigroups by Klaus-Jochen Engel,Rainer Nagel Pdf

The book offers a direct and up-to-date introduction to the theory of one-parameter semigroups of linear operators on Banach spaces. The book is intended for students and researchers who want to become acquainted with the concept of semigroups.

Author : András Bátkai,Marjeta Kramar Fijavž,Abdelaziz Rhandi
Publisher : Birkhäuser
Page : 364 pages
File Size : 55,6 Mb
Release : 2017-02-13
Category : Mathematics
ISBN : 9783319428130

Get Book

Positive Operator Semigroups by András Bátkai,Marjeta Kramar Fijavž,Abdelaziz Rhandi Pdf

This book gives a gentle but up-to-date introduction into the theory of operator semigroups (or linear dynamical systems), which can be used with great success to describe the dynamics of complicated phenomena arising in many applications. Positivity is a property which naturally appears in physical, chemical, biological or economic processes. It adds a beautiful and far reaching mathematical structure to the dynamical systems and operators describing these processes. In the first part, the finite dimensional theory in a coordinate-free way is developed, which is difficult to find in literature. This is a good opportunity to present the main ideas of the Perron-Frobenius theory in a way which can be used in the infinite dimensional situation. Applications to graph matrices, age structured population models and economic models are discussed. The infinite dimensional theory of positive operator semigroups with their spectral and asymptotic theory is developed in the second part. Recent applications illustrate the theory, like population equations, neutron transport theory, delay equations or flows in networks. Each chapter is accompanied by a large set of exercises. An up-to-date bibliography and a detailed subject index help the interested reader. The book is intended primarily for graduate and master students. The finite dimensional part, however, can be followed by an advanced bachelor with a solid knowledge of linear algebra and calculus.

Author : Shmuel Kantorovitz
Publisher : Springer Science & Business Media
Page : 269 pages
File Size : 42,6 Mb
Release : 2009-10-23
Category : Electronic
ISBN : 9780817649357

Get Book

na by Shmuel Kantorovitz Pdf

Author : Jack K. Hale
Publisher : American Mathematical Soc.
Page : 210 pages
File Size : 51,9 Mb
Release : 2010-01-04
Category : Mathematics
ISBN : 9780821849347

Get Book

Asymptotic Behavior of Dissipative Systems by Jack K. Hale Pdf

This monograph reports the advances that have been made in the area by the author and many other mathematicians; it is an important source of ideas for the researchers interested in the subject. --Zentralblatt MATH Although advanced, this book is a very good introduction to the subject, and the reading of the abstract part, which is elegant, is pleasant. ... this monograph will be of valuable interest for those who aim to learn in the very rapidly growing subject of infinite-dimensional dissipative dynamical systems. --Mathematical Reviews This book is directed at researchers in nonlinear ordinary and partial differential equations and at those who apply these topics to other fields of science. About one third of the book focuses on the existence and properties of the flow on the global attractor for a discrete or continuous dynamical system. The author presents a detailed discussion of abstract properties and examples of asymptotically smooth maps and semigroups. He also covers some of the continuity properties of the global attractor under perturbation, its capacity and Hausdorff dimension, and the stability of the flow on the global attractor under perturbation. The remainder of the book deals with particular equations occurring in applications and especially emphasizes delay equations, reaction-diffusion equations, and the damped wave equations. In each of the examples presented, the author shows how to verify the existence of a global attractor, and, for several examples, he discusses some properties of the flow on the global attractor.

Author : Amnon Pazy
Publisher : Springer Science & Business Media
Page : 289 pages
File Size : 50,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461255611

Get Book

Semigroups of Linear Operators and Applications to Partial Differential Equations by Amnon Pazy Pdf

Since the characterization of generators of C0 semigroups was established in the 1940s, semigroups of linear operators and its neighboring areas have developed into an abstract theory that has become a necessary discipline in functional analysis and differential equations. This book presents that theory and its basic applications, and the last two chapters give a connected account of the applications to partial differential equations.

Author : David Applebaum
Publisher : Cambridge University Press
Page : 235 pages
File Size : 54,8 Mb
Release : 2019-08-15
Category : Mathematics
ISBN : 9781108483094

Get Book

Semigroups of Linear Operators by David Applebaum Pdf

Provides a graduate-level introduction to the theory of semigroups of operators.

Author : Pierre Magal,Shigui Ruan
Publisher : Springer
Page : 543 pages
File Size : 50,9 Mb
Release : 2018-11-21
Category : Mathematics
ISBN : 9783030015060

Get Book

Theory and Applications of Abstract Semilinear Cauchy Problems by Pierre Magal,Shigui Ruan Pdf

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 : Jacek Banasiak,Mustapha Mokhtar-Kharroubi
Publisher : Springer
Page : 493 pages
File Size : 52,7 Mb
Release : 2014-11-07
Category : Mathematics
ISBN : 9783319113227

Get Book

Evolutionary Equations with Applications in Natural Sciences by Jacek Banasiak,Mustapha Mokhtar-Kharroubi Pdf

With the unifying theme of abstract evolutionary equations, both linear and nonlinear, in a complex environment, the book presents a multidisciplinary blend of topics, spanning the fields of theoretical and applied functional analysis, partial differential equations, probability theory and numerical analysis applied to various models coming from theoretical physics, biology, engineering and complexity theory. Truly unique features of the book are: the first simultaneous presentation of two complementary approaches to fragmentation and coagulation problems, by weak compactness methods and by using semigroup techniques, comprehensive exposition of probabilistic methods of analysis of long term dynamics of dynamical systems, semigroup analysis of biological problems and cutting edge pattern formation theory. The book will appeal to postgraduate students and researchers specializing in applications of mathematics to problems arising in natural sciences and engineering.