Vector Valued Laplace Transforms And Cauchy Problems
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Vector Valued Laplace Transforms And Cauchy Problems
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Author : Wolfgang Arendt
language : en
Publisher: Springer Science & Business Media
Release Date : 2001
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 2001 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>.
Vector Valued Laplace Transforms And Cauchy Problems
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Author : Wolfgang Arendt
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-04-05
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 2011-04-05 with Mathematics categories.
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
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Author : Wolfgang Arendt
language : en
Publisher:
Release Date : 2011-04-07
Vector Valued Laplace Transforms And Cauchy Problems written by Wolfgang Arendt and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-04-07 with categories.
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>. .
Differential Equations In Banach Spaces
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Author : Giovanni Dore
language : en
Publisher: CRC Press
Release Date : 2020-10-07
Differential Equations In Banach Spaces written by Giovanni Dore and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-07 with Mathematics categories.
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.
Differential Equations In Banach Spaces
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Author : Giovanni Dore
language : en
Publisher: CRC Press
Release Date : 2020-10-08
Differential Equations In Banach Spaces written by Giovanni Dore and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-08 with Mathematics categories.
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.
Semigroup Theory And Evolution Equations
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Author : Philippe Clement
language : en
Publisher: CRC Press
Release Date : 2023-05-31
Semigroup Theory And Evolution Equations written by Philippe Clement and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-31 with Mathematics categories.
Proceedings of the Second International Conference on Trends in Semigroup Theory and Evolution Equations held Sept. 1989, Delft University of Technology, the Netherlands. Papers deal with recent developments in semigroup theory (e.g., positive, dual, integrated), and nonlinear evolution equations (e
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.
Semigroups Of Operators Theory And Applications
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Author : A.V. Balakrishnan
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Semigroups Of Operators Theory And Applications written by A.V. Balakrishnan and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
These Proceedings comprise the bulk of the papers presented at the Inter national Conference on Semigroups of Opemtors: Theory and Contro~ held 14-18 December 1998, Newport Beach, California, U.S.A. The intent of the Conference was to highlight recent advances in the the ory of Semigroups of Operators which provides the abstract framework for the time-domain solutions of time-invariant boundary-value/initial-value problems of partial differential equations. There is of course a firewall between the ab stract theory and the applications and one of the Conference aims was to bring together both in the hope that it may be of value to both communities. In these days when all scientific activity is judged by its value on "dot com" it is not surprising that mathematical analysis that holds no promise of an immediate commercial product-line, or even a software tool-box, is not high in research priority. We are particularly pleased therefore that the National Science Foundation provided generous financial support without which this Conference would have been impossible to organize. Our special thanks to Dr. Kishan Baheti, Program Manager.
Functional Analytic Methods For Evolution Equations
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Author : Giuseppe Da Prato
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-09-22
Functional Analytic Methods For Evolution Equations written by Giuseppe Da Prato 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 2004-09-22 with Mathematics categories.
This book consists of five introductory contributions by leading mathematicians on the functional analytic treatment of evolutions equations. In particular the contributions deal with Markov semigroups, maximal L^p-regularity, optimal control problems for boundary and point control systems, parabolic moving boundary problems and parabolic nonautonomous evolution equations. The book is addressed to PhD students, young researchers and mathematicians doing research in one of the above topics.