Vector Valued Laplace Transforms And Cauchy Problems

Download Vector Valued Laplace Transforms And Cauchy Problems full books in PDF, epub, and Kindle. Read online Vector Valued Laplace Transforms And Cauchy Problems ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!

Vector-valued Laplace Transforms and Cauchy Problems

Author : Wolfgang Arendt
Publisher : Springer Science & Business Media
ISBN 13 : 3034800878
Total Pages : 540 pages
Book Rating : 4.0/5 (348 download)

DOWNLOAD NOW!

Book Synopsis Vector-valued Laplace Transforms and Cauchy Problems by : Wolfgang Arendt

Download or read book Vector-valued Laplace Transforms and Cauchy Problems written by Wolfgang Arendt and published by Springer Science & Business Media. This book was released on 2011-04-05 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph gives a systematic account of the theory of vector-valued Laplace transforms, ranging from representation theory to Tauberian theorems. In parallel, the theory of linear Cauchy problems and semigroups of operators is developed completely in the spirit of Laplace transforms. Existence and uniqueness, regularity, approximation and above all asymptotic behaviour of solutions are studied. Diverse applications to partial differential equations are given. The book contains an introduction to the Bochner integral and several appendices on background material. It is addressed to students and researchers interested in evolution equations, Laplace and Fourier transforms, and functional analysis. The second edition contains detailed notes on the developments in the last decade. They include, for instance, a new characterization of well-posedness of abstract wave equations in Hilbert space due to M. Crouzeix. Moreover new quantitative results on asymptotic behaviour of Laplace transforms have been added. The references are updated and some errors have been corrected.

Vector-Valued Laplace Transforms and Cauchy Problems

Author : Wolfgang Arendt
Publisher :
ISBN 13 : 9783034800884
Total Pages : 554 pages
Book Rating : 4.8/5 (8 download)

DOWNLOAD NOW!

Book Synopsis Vector-Valued Laplace Transforms and Cauchy Problems by : Wolfgang Arendt

Download or read book Vector-Valued Laplace Transforms and Cauchy Problems written by Wolfgang Arendt and published by . This book was released on 2011-04-07 with total page 554 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Vector-valued Laplace Transforms and Cauchy Problems

Author : Wolfgang Arendt
Publisher : Springer Science & Business Media
ISBN 13 : 3034850751
Total Pages : 526 pages
Book Rating : 4.0/5 (348 download)

DOWNLOAD NOW!

Book Synopsis Vector-valued Laplace Transforms and Cauchy Problems by : Wolfgang Arendt

Download or read book Vector-valued Laplace Transforms and Cauchy Problems written by Wolfgang Arendt and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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>. .

The Cauchy Problem for Higher Order Abstract Differential Equations

Author : Ti-Jun Xiao
Publisher : Springer Science & Business Media
ISBN 13 : 9783540652380
Total Pages : 324 pages
Book Rating : 4.6/5 (523 download)

DOWNLOAD NOW!

Book Synopsis The Cauchy Problem for Higher Order Abstract Differential Equations by : Ti-Jun Xiao

Download or read book The Cauchy Problem for Higher Order Abstract Differential Equations written by Ti-Jun Xiao and published by Springer Science & Business Media. This book was released on 1998-11-18 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Stochastic Cauchy Problems in Infinite Dimensions

Author : Irina V. Melnikova
Publisher : CRC Press
ISBN 13 : 1315360268
Total Pages : 232 pages
Book Rating : 4.3/5 (153 download)

DOWNLOAD NOW!

Book Synopsis Stochastic Cauchy Problems in Infinite Dimensions by : Irina V. Melnikova

Download or read book Stochastic Cauchy Problems in Infinite Dimensions written by Irina V. Melnikova and published by CRC Press. This book was released on 2018-09-03 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic Cauchy Problems in Infinite Dimensions: Generalized and Regularized Solutions presents stochastic differential equations for random processes with values in Hilbert spaces. Accessible to non-specialists, the book explores how modern semi-group and distribution methods relate to the methods of infinite-dimensional stochastic analysis. It also shows how the idea of regularization in a broad sense pervades all these methods and is useful for numerical realization and applications of the theory. The book presents generalized solutions to the Cauchy problem in its initial form with white noise processes in spaces of distributions. It also covers the "classical" approach to stochastic problems involving the solution of corresponding integral equations. The first part of the text gives a self-contained introduction to modern semi-group and abstract distribution methods for solving the homogeneous (deterministic) Cauchy problem. In the second part, the author solves stochastic problems using semi-group and distribution methods as well as the methods of infinite-dimensional stochastic analysis.

Theory and Applications of Abstract Semilinear Cauchy Problems

Author : Pierre Magal
Publisher : Springer
ISBN 13 : 3030015068
Total Pages : 543 pages
Book Rating : 4.0/5 (3 download)

DOWNLOAD NOW!

Book Synopsis Theory and Applications of Abstract Semilinear Cauchy Problems by : Pierre Magal

Download or read book Theory and Applications of Abstract Semilinear Cauchy Problems written by Pierre Magal and published by Springer. This book was released on 2018-11-21 with total page 543 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Almost Periodic and Almost Automorphic Solutions to Integro-Differential Equations

Author : Marko Kostić
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110641852
Total Pages : 372 pages
Book Rating : 4.1/5 (16 download)

DOWNLOAD NOW!

Book Synopsis Almost Periodic and Almost Automorphic Solutions to Integro-Differential Equations by : Marko Kostić

Download or read book Almost Periodic and Almost Automorphic Solutions to Integro-Differential Equations written by Marko Kostić and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-05-06 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses almost periodic and almost automorphic solutions to abstract integro-differential Volterra equations that are degenerate in time, and in particular equations whose solutions are governed by (degenerate) solution operator families with removable singularities at zero. It particularly covers abstract fractional equations and inclusions with multivalued linear operators as well as abstract fractional semilinear Cauchy problems.

$\mathcal {R}$-Boundedness, Fourier Multipliers and Problems of Elliptic and Parabolic Type

$Download $\mathcal {R}$-Boundedness, Fourier Multipliers and Problems of Elliptic and Parabolic Type PDF Online Free$

Author : Robert Denk
Publisher : American Mathematical Soc.
ISBN 13 : 0821833782
Total Pages : 130 pages
Book Rating : 4.8/5 (218 download)

DOWNLOAD NOW!

Book Synopsis $\mathcal {R}$-Boundedness, Fourier Multipliers and Problems of Elliptic and Parabolic Type by : Robert Denk

Download or read book $\mathcal {R}$-Boundedness, Fourier Multipliers and Problems of Elliptic and Parabolic Type written by Robert Denk and published by American Mathematical Soc.. This book was released on 2003 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: The property of maximal $L_p$-regularity for parabolic evolution equations is investigated via the concept of $\mathcal R$-sectorial operators and operator-valued Fourier multipliers. As application, we consider the $L_q$-realization of an elliptic boundary value problem of order $2m$ with operator-valued coefficients subject to general boundary conditions. We show that there is maximal $L_p$-$L_q$-regularity for the solution of the associated Cauchy problem provided the top order coefficients are bounded and uniformly continuous.

Infinite Dimensional Dynamical Systems

Author : John Mallet-Paret
Publisher : Springer Science & Business Media
ISBN 13 : 1461445221
Total Pages : 495 pages
Book Rating : 4.4/5 (614 download)

DOWNLOAD NOW!

Book Synopsis Infinite Dimensional Dynamical Systems by : John Mallet-Paret

Download or read book Infinite Dimensional Dynamical Systems written by John Mallet-Paret and published by Springer Science & Business Media. This book was released on 2012-10-11 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection covers a wide range of topics of infinite dimensional dynamical systems generated by parabolic partial differential equations, hyperbolic partial differential equations, solitary equations, lattice differential equations, delay differential equations, and stochastic differential equations. Infinite dimensional dynamical systems are generated by evolutionary equations describing the evolutions in time of systems whose status must be depicted in infinite dimensional phase spaces. Studying the long-term behaviors of such systems is important in our understanding of their spatiotemporal pattern formation and global continuation, and has been among major sources of motivation and applications of new developments of nonlinear analysis and other mathematical theories. Theories of the infinite dimensional dynamical systems have also found more and more important applications in physical, chemical, and life sciences. This book collects 19 papers from 48 invited lecturers to the International Conference on Infinite Dimensional Dynamical Systems held at York University, Toronto, in September of 2008. As the conference was dedicated to Professor George Sell from University of Minnesota on the occasion of his 70th birthday, this collection reflects the pioneering work and influence of Professor Sell in a few core areas of dynamical systems, including non-autonomous dynamical systems, skew-product flows, invariant manifolds theory, infinite dimensional dynamical systems, approximation dynamics, and fluid flows.

The Functional Calculus for Sectorial Operators

Author : Markus Haase
Publisher : Springer Science & Business Media
ISBN 13 : 3764376988
Total Pages : 399 pages
Book Rating : 4.7/5 (643 download)

DOWNLOAD NOW!

Book Synopsis The Functional Calculus for Sectorial Operators by : Markus Haase

Download or read book The Functional Calculus for Sectorial Operators written by Markus Haase and published by Springer Science & Business Media. This book was released on 2006-08-18 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a systematic and partly axiomatic treatment of the holomorphic functional calculus for unbounded sectorial operators. The account is generic so that it can be used to construct and interrelate holomorphic functional calculi for other types of unbounded operators. Particularly, an elegant unified approach to holomorphic semigroups is obtained. The last chapter describes applications to PDE, evolution equations and approximation theory as well as the connection with harmonic analysis.

Center Manifolds for Semilinear Equations with Non-Dense Domain and Applications to Hopf Bifurcation in Age Structured Models

Author : Pierre Magal
Publisher : American Mathematical Soc.
ISBN 13 : 0821846531
Total Pages : 84 pages
Book Rating : 4.8/5 (218 download)

DOWNLOAD NOW!

Book Synopsis Center Manifolds for Semilinear Equations with Non-Dense Domain and Applications to Hopf Bifurcation in Age Structured Models by : Pierre Magal

Download or read book Center Manifolds for Semilinear Equations with Non-Dense Domain and Applications to Hopf Bifurcation in Age Structured Models written by Pierre Magal and published by American Mathematical Soc.. This book was released on 2009 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt: Several types of differential equations, such as delay differential equations, age-structure models in population dynamics, evolution equations with boundary conditions, can be written as semilinear Cauchy problems with an operator which is not densely defined in its domain. The goal of this paper is to develop a center manifold theory for semilinear Cauchy problems with non-dense domain. Using Liapunov-Perron method and following the techniques of Vanderbauwhede et al. in treating infinite dimensional systems, the authors study the existence and smoothness of center manifolds for semilinear Cauchy problems with non-dense domain. As an application, they use the center manifold theorem to establish a Hopf bifurcation theorem for age structured models.

Mathematical Analysis of the Navier-Stokes Equations

Author : Matthias Hieber
Publisher : Springer Nature
ISBN 13 : 3030362264
Total Pages : 471 pages
Book Rating : 4.0/5 (33 download)

DOWNLOAD NOW!

Book Synopsis Mathematical Analysis of the Navier-Stokes Equations by : Matthias Hieber

Download or read book Mathematical Analysis of the Navier-Stokes Equations written by Matthias Hieber and published by Springer Nature. This book was released on 2020-04-28 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects together a unique set of articles dedicated to several fundamental aspects of the Navier–Stokes equations. As is well known, understanding the mathematical properties of these equations, along with their physical interpretation, constitutes one of the most challenging questions of applied mathematics. Indeed, the Navier-Stokes equations feature among the Clay Mathematics Institute's seven Millennium Prize Problems (existence of global in time, regular solutions corresponding to initial data of unrestricted magnitude). The text comprises three extensive contributions covering the following topics: (1) Operator-Valued H∞-calculus, R-boundedness, Fourier multipliers and maximal Lp-regularity theory for a large, abstract class of quasi-linear evolution problems with applications to Navier–Stokes equations and other fluid model equations; (2) Classical existence, uniqueness and regularity theorems of solutions to the Navier–Stokes initial-value problem, along with space-time partial regularity and investigation of the smoothness of the Lagrangean flow map; and (3) A complete mathematical theory of R-boundedness and maximal regularity with applications to free boundary problems for the Navier–Stokes equations with and without surface tension. Offering a general mathematical framework that could be used to study fluid problems and, more generally, a wide class of abstract evolution equations, this volume is aimed at graduate students and researchers who want to become acquainted with fundamental problems related to the Navier–Stokes equations.

Convergence of One-parameter Operator Semigroups

Author : Adam Bobrowski
Publisher : Cambridge University Press
ISBN 13 : 1107137438
Total Pages : 453 pages
Book Rating : 4.1/5 (71 download)

DOWNLOAD NOW!

Book Synopsis Convergence of One-parameter Operator Semigroups by : Adam Bobrowski

Download or read book Convergence of One-parameter Operator Semigroups written by Adam Bobrowski and published by Cambridge University Press. This book was released on 2016-07-14 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents the classical theory of convergence of semigroups and looks at how it applies to real-world phenomena.

Recent Developments in Evolution Equations

Author : G F Roach
Publisher : CRC Press
ISBN 13 : 9780582246690
Total Pages : 268 pages
Book Rating : 4.2/5 (466 download)

DOWNLOAD NOW!

Book Synopsis Recent Developments in Evolution Equations by : G F Roach

Download or read book Recent Developments in Evolution Equations written by G F Roach and published by CRC Press. This book was released on 1995-04-28 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the majority of talks given at an International Converence held recently at the University of Strathclyde in Glasgow. The works presented focus on the analysis of mathematical models of systems evolving with time. The main topics are semigroups and related subjects connected with applications to partial differential equations of evolution type. Topics of particular interest include spectral and asymptotic properties of semigroups, B evolution scattering theory, and coagulation fragmentation phenomena.

Analytic Methods for Coagulation-Fragmentation Models, Volume I

Author : Jacek Banasiak
Publisher : CRC Press
ISBN 13 : 1351650467
Total Pages : 330 pages
Book Rating : 4.3/5 (516 download)

DOWNLOAD NOW!

Book Synopsis Analytic Methods for Coagulation-Fragmentation Models, Volume I by : Jacek Banasiak

Download or read book Analytic Methods for Coagulation-Fragmentation Models, Volume I written by Jacek Banasiak and published by CRC Press. This book was released on 2019-09-04 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analytic Methods for Coagulation-Fragmentation Models is a two-volume set that provides a comprehensive exposition of the mathematical analysis of coagulation-fragmentation models. Initially, an in-depth survey of coagulation-fragmentation processes is presented, together with an account of relevant early results obtained on the associated model equations. These provide motivation for the subsequent detailed treatment of more up-to-date investigations which have led to significant theoretical developments on topics such as solvability and the long-term behaviour of solutions. To make the account as self-contained as possible, the mathematical tools that feature prominently in these modern treatments are introduced at appropriate places. The main theme of Volume I is the analysis of linear fragmentation models, with Volume II devoted to processes that involve the nonlinear contribution of coagulation. Features of Volume I: The main models of the theory together with their derivations and early methods of solution A detailed presentation of the operator theoretical methods and semigroup theory that play an essential role in the theory of fragmentation processes A comprehensive theory of fragmentation processes, including fragmentation with growth and decay in both the discrete and continuous particle size cases An analytical explanation of the `pathologies’ of the fragmentation equation, such as the shattering phase transition and non-uniqueness of solutions An analysis of the long-term dynamics of the discrete size fragmentation equation with growth

Topics in Nonlinear Analysis

Author : Joachim Escher
Publisher : Birkhäuser
ISBN 13 : 3034887655
Total Pages : 741 pages
Book Rating : 4.0/5 (348 download)

DOWNLOAD NOW!

Book Synopsis Topics in Nonlinear Analysis by : Joachim Escher

Download or read book Topics in Nonlinear Analysis written by Joachim Escher and published by Birkhäuser. This book was released on 2012-12-06 with total page 741 pages. Available in PDF, EPUB and Kindle. Book excerpt: Herbert Amann's work is distinguished and marked by great lucidity and deep mathematical understanding. The present collection of 31 research papers, written by highly distinguished and accomplished mathematicians, reflect his interest and lasting influence in various fields of analysis such as degree and fixed point theory, nonlinear elliptic boundary value problems, abstract evolutions equations, quasi-linear parabolic systems, fluid dynamics, Fourier analysis, and the theory of function spaces. Contributors are A. Ambrosetti, S. Angenent, W. Arendt, M. Badiale, T. Bartsch, Ph. Bénilan, Ph. Clément, E. Faöangová, M. Fila, D. de Figueiredo, G. Gripenberg, G. Da Prato, E.N. Dancer, D. Daners, E. DiBenedetto, D.J. Diller, J. Escher, G.P. Galdi, Y. Giga, T. Hagen, D.D. Hai, M. Hieber, H. Hofer, C. Imbusch, K. Ito, P. Krejcí, S.-O. Londen, A. Lunardi, T. Miyakawa, P. Quittner, J. Prüss, V.V. Pukhnachov, P.J. Rabier, P.H. Rabinowitz, M. Renardy, B. Scarpellini, B.J. Schmitt, K. Schmitt, G. Simonett, H. Sohr, V.A. Solonnikov, J. Sprekels, M. Struwe, H. Triebel, W. von Wahl, M. Wiegner, K. Wysocki, E. Zehnder and S. Zheng.

Differential Equations in Banach Spaces

Author : Giovanni Dore
Publisher : CRC Press
ISBN 13 : 1000153657
Total Pages : 290 pages
Book Rating : 4.0/5 (1 download)

DOWNLOAD NOW!

Book Synopsis Differential Equations in Banach Spaces by : Giovanni Dore

Download or read book Differential Equations in Banach Spaces written by Giovanni Dore and published by CRC Press. This book was released on 2020-10-08 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This reference - based on the Conference on Differential Equations, held in Bologna - provides information on current research in parabolic and hyperbolic differential equations. Presenting methods and results in semigroup theory and their applications to evolution equations, this book focuses on topics including: abstract parabolic and hyperbolic linear differential equations; nonlinear abstract parabolic equations; holomorphic semigroups; and Volterra operator integral equations.;With contributions from international experts, Differential Equations in Banach Spaces is intended for research mathematicians in functional analysis, partial differential equations, operator theory and control theory; and students in these disciplines.