Abstract Cauchy Problems
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Theory And Applications Of Abstract Semilinear Cauchy Problems
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Author : Pierre Magal
language : en
Publisher: Springer
Release Date : 2018-11-21
Theory And Applications Of Abstract Semilinear Cauchy Problems written by Pierre Magal and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-21 with Mathematics categories.
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.
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.
Abstract Cauchy Problems
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Author : Irina V. Melnikova
language : en
Publisher: Chapman and Hall/CRC
Release Date : 2001-03-27
Abstract Cauchy Problems written by Irina V. Melnikova and has been published by Chapman and Hall/CRC 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 regularization methods. Semigroup and distribution methods restore well-posedness, in a modern weak sense. Regularization methods provide approximate solutions to ill-posed problems. Although these approaches were extensively developed over the last decades by many researchers, nowhere could one find a comprehensive treatment of all three approaches. Abstract Cauchy Problems: Three Approaches provides an innovative, self-contained account of these methods and, furthermore, demonstrates and studies some of the profound connections between them. The authors discuss the application of different methods not only to the Cauchy problem that is not well-posed in the classical sense, but also to important generalizations: the Cauchy problem for inclusion and the Cauchy problem for second order equations. Accessible to nonspecialists and beginning graduate students, this volume brings together many different ideas to serve as a reference on modern methods for abstract linear evolution equations.
Vector Valued Laplace Transforms And Cauchy Problems
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Author : Wolfgang Arendt
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Vector Valued Laplace Transforms And Cauchy Problems written by Wolfgang Arendt 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 2013-11-11 with Mathematics categories.
Linear evolution equations in Banach spaces have seen important developments in the last two decades. This is due to the many different applications in the theory of partial differential equations, probability theory, mathematical physics, and other areas, and also to the development of new techniques. One important technique is given by the Laplace transform. It played an important role in the early development of semigroup theory, as can be seen in the pioneering monograph by Rille and Phillips [HP57]. But many new results and concepts have come from Laplace transform techniques in the last 15 years. In contrast to the classical theory, one particular feature of this method is that functions with values in a Banach space have to be considered. The aim of this book is to present the theory of linear evolution equations in a systematic way by using the methods of vector-valued Laplace transforms. It is simple to describe the basic idea relating these two subjects. Let A be a closed linear operator on a Banach space X. The Cauchy problern defined by A is the initial value problern (t 2 0), (CP) {u'(t) = Au(t) u(O) = x, where x E X is a given initial value. If u is an exponentially bounded, continuous function, then we may consider the Laplace transform 00 u(>. ) = 1 e-). . tu(t) dt of u for large real>. .
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
Singular And Degenerate Cauchy Problems
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Author :
language : en
Publisher: Academic Press
Release Date : 1977-01-13
Singular And Degenerate Cauchy Problems written by and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977-01-13 with Mathematics categories.
In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; andmethods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.As a result, the book represents a blend of new methods in general computational analysis,and specific, but also generic, techniques for study of systems theory ant its particularbranches, such as optimal filtering and information compression.- Best operator approximation,- Non-Lagrange interpolation,- Generic Karhunen-Loeve transform- Generalised low-rank matrix approximation- Optimal data compression- Optimal nonlinear filtering
Abstract Cauchy Problems And Functionnal Differential Equations
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Author :
language : en
Publisher:
Release Date : 1981
Abstract Cauchy Problems And Functionnal Differential Equations written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with categories.
Abstract Cauchy Problems And Functional Differential Equations
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Author : F. Kappel
language : en
Publisher: Pitman Publishing
Release Date : 1981
Abstract Cauchy Problems And Functional Differential Equations written by F. Kappel and has been published by Pitman Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Mathematics categories.
Abstract Cauchy Problems And Functional Differential Equations
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Author :
language : en
Publisher:
Release Date : 1981
Abstract Cauchy Problems And Functional Differential Equations written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with categories.
Abstract Differential Equations And Nonlinear Mixed Problems
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Author : Tosio Kato
language : en
Publisher: Edizioni della Normale
Release Date : 1988-10-01
Abstract Differential Equations And Nonlinear Mixed Problems written by Tosio Kato and has been published by Edizioni della Normale this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-10-01 with Mathematics categories.
The present article is based on the Fermi Lectures I gave in May, 1985, at Scuola Normale Superiore, Pisa, in which I discussed various methods for solving the Cauchy problem for abstract nonlinear differential equations of evolution type. Here I present a detailed exposition of one of these methods, which deals with “elliptic-hyperbolic” equations in the abstract form and which has applications, among other things, to mixed initial-boundary value problems for certain nonlinear partial differential equations, such as elastodynamic and Schrödinger equations.