The Cauchy Problem For Higher Order Abstract Differential Equations
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The Cauchy Problem For Higher Order Abstract Differential Equations
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Author : Ti-Jun Xiao
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-11-18
The Cauchy Problem For Higher Order Abstract Differential Equations written by Ti-Jun Xiao and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-11-18 with Mathematics categories.
This monograph is the first systematic exposition of the theory of the Cauchy problem for higher order abstract linear differential equations, which covers all the main aspects of the developed theory. The main results are complete with detailed proofs and established recently, containing the corresponding theorems for first and incomplete second order cases and therefore for operator semigroups and cosine functions. They will find applications in many fields. The special power of treating the higher order problems directly is demonstrated, as well as that of the vector-valued Laplace transforms in dealing with operator differential equations and operator families. The reader is expected to have a knowledge of complex and functional analysis.
The Cauchy Problem For Higher Order Abstract Differential Equations
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Author : Ti-Jun Xiao
language : en
Publisher: Springer
Release Date : 2013-12-11
The Cauchy Problem For Higher Order Abstract Differential Equations written by Ti-Jun Xiao and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-11 with Mathematics categories.
The main purpose of this book is to present the basic theory and some recent de velopments concerning the Cauchy problem for higher order abstract differential equations u(n)(t) + ~ AiU(i)(t) = 0, t ~ 0, { U(k)(O) = Uk, 0 ~ k ~ n-l. where AQ, Ab . . . , A - are linear operators in a topological vector space E. n 1 Many problems in nature can be modeled as (ACP ). For example, many n initial value or initial-boundary value problems for partial differential equations, stemmed from mechanics, physics, engineering, control theory, etc. , can be trans lated into this form by regarding the partial differential operators in the space variables as operators Ai (0 ~ i ~ n - 1) in some function space E and letting the boundary conditions (if any) be absorbed into the definition of the space E or of the domain of Ai (this idea of treating initial value or initial-boundary value problems was discovered independently by E. Hille and K. Yosida in the forties). The theory of (ACP ) is closely connected with many other branches of n mathematics. Therefore, the study of (ACPn) is important for both theoretical investigations and practical applications. Over the past half a century, (ACP ) has been studied extensively.
The Cauchy Problem For Higher Order Abstract Differential Equations
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Author : Ti-Jun Xiao
language : en
Publisher:
Release Date : 2014-09-01
The Cauchy Problem For Higher Order Abstract Differential Equations written by Ti-Jun Xiao and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-01 with categories.
Differential Equations And Control Theory
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Author : Z. Deng
language : en
Publisher: CRC Press
Release Date : 2020-11-25
Differential Equations And Control Theory written by Z. Deng and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-25 with Mathematics categories.
This work presents the proceedings from the International Conference on Differential Equations and Control Theory, held recently in Wuhan, China. It provides an overview of current developments in a range of topics including dynamical systems, optimal control theory, stochastic control, chaos, fractals, wavelets and ordinary, partial, functional and stochastic differential equations.
The Cauchy Problem
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Author : Hector O. Fattorini
language : en
Publisher: Cambridge University Press
Release Date : 1983
The Cauchy Problem written by Hector O. Fattorini and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Mathematics categories.
This volume deals with the Cauchy or initial value problem for linear differential equations. It treats in detail some of the applications of linear space methods to partial differential equations, especially the equations of mathematical physics such as the Maxwell, Schrödinger and Dirac equations. Background material presented in the first chapter makes the book accessible to mathematicians and physicists who are not specialists in this area as well as to graduate students.
Abstract Cauchy Problems
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Author : Irina V. Melnikova
language : en
Publisher: CRC Press
Release Date : 2001-03-27
Abstract Cauchy Problems written by Irina V. Melnikova and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-03-27 with Mathematics categories.
Although the theory of well-posed Cauchy problems is reasonably understood, ill-posed problems-involved in a numerous mathematical models in physics, engineering, and finance- can be approached in a variety of ways. Historically, there have been three major strategies for dealing with such problems: semigroup, abstract distribution, and regularizat
Stable Approximate Evaluation Of Unbounded Operators
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Author : C. W. Groetsch
language : en
Publisher: Springer Science & Business Media
Release Date : 2007
Stable Approximate Evaluation Of Unbounded Operators written by C. W. Groetsch and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
Spectral theory of bounded linear operators teams up with von Neumann’s theory of unbounded operators in this monograph to provide a general framework for the study of stable methods for the evaluation of unbounded operators. An introductory chapter provides numerous illustrations of unbounded linear operators that arise in various inverse problems of mathematical physics. Before the general theory of stabilization methods is developed, an extensive exposition of the necessary background material from the theory of operators on Hilbert space is provided. Several specific stabilization methods are studied in detail, with particular attention to the Tikhonov-Morozov method and its iterated version.
Local And Semi Local Bifurcations In Hamiltonian Dynamical Systems
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Author : Heinz Hanßmann
language : en
Publisher: Springer
Release Date : 2006-10-18
Local And Semi Local Bifurcations In Hamiltonian Dynamical Systems written by Heinz Hanßmann and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-10-18 with Mathematics categories.
This book demonstrates that while elliptic and hyperbolic tori determine the distribution of maximal invariant tori, they themselves form n-parameter families. Therefore, torus bifurcations of high co-dimension may be found in a single given Hamiltonian system, absent untypical conditions or external parameters. The text moves logically from the integrable case, in which symmetries allow for reduction to bifurcating equilibria, to non-integrability, where smooth parametrisations must be replaced by Cantor sets.
Matrix Inequalities
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Author : Xingzhi Zhan
language : en
Publisher: Springer
Release Date : 2004-10-19
Matrix Inequalities written by Xingzhi Zhan and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-10-19 with Mathematics categories.
The main purpose of this monograph is to report on recent developments in the field of matrix inequalities, with emphasis on useful techniques and ingenious ideas. Among other results this book contains the affirmative solutions of eight conjectures. Many theorems unify or sharpen previous inequalities. The author's aim is to streamline the ideas in the literature. The book can be read by research workers, graduate students and advanced undergraduates.
Monotone Random Systems Theory And Applications
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Author : Igor Chueshov
language : en
Publisher: Springer
Release Date : 2004-10-11
Monotone Random Systems Theory And Applications written by Igor Chueshov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-10-11 with Mathematics categories.
The aim of this book is to present a recently developed approach suitable for investigating a variety of qualitative aspects of order-preserving random dynamical systems and to give the background for further development of the theory. The main objects considered are equilibria and attractors. The effectiveness of this approach is demonstrated by analysing the long-time behaviour of some classes of random and stochastic ordinary differential equations which arise in many applications.