Overview

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.

Full Product Details

Author:   Ti-Jun Xiao ,  Jin Liang
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   1998 ed.
Volume:   1701
Dimensions:   Width: 15.50cm , Height: 1.70cm , Length: 23.50cm
Weight:   1.010kg
ISBN:  

9783540652380

ISBN 10:   3540652388
Pages:   300
Publication Date:   18 November 1998
Audience:   College/higher education ,  General/trade ,  Postgraduate, Research & Scholarly ,  General
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

Laplace transforms and operator families in locally convex spaces.- Wellposedness and solvability.- Generalized wellposedness.- Analyticity and parabolicity.- Exponential growth bound and exponential stability.- Differentiability and norm continuity.- Almost periodicity.- Appendices: A1 Fractional powers of non-negative operators.- A2 Strongly continuous semigroups and cosine functions.- Bibliography.- Index.- Symbols.

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