The Cauchy problem for higher-order abstract differential equations /

The Cauchy problem for higher-order abstract differential equations /

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Bibliographic Details
Author / Creator:	Xiao, Ti-Jun, 1964-
Imprint:	Berlin ; New York : Springer, ©1998.
Description:	1 online resource (xii, 300 pages).
Language:	English
Series:	Lecture notes in mathematics, 0075-8434 ; 1701 Lecture notes in mathematics (Springer-Verlag) ; 1701.
Subject:	Differential equations. Cauchy problem. Banach spaces. Hilbert space. Banach spaces. Cauchy problem. Differential equations. Hilbert space.
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/11065986

Hidden Bibliographic Details
Other authors / contributors:	Liang, Jin, 1964-
ISBN:	9783540494799 3540494790 3540652388 9783540652380
Notes:	Includes bibliographical references (pages 269-297) and index. Print version record.
Summary:	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.
Other form:	Print version: Xiao, Ti-Jun, 1964- Cauchy problem for higher-order abstract differential equations. Berlin ; New York : Springer, ©1998 3540652388

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.