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

Description
Summary:	The main purpose of this book is to present the basic theory and some recent de velopments concerning the Cauchy problem for higher order abstract differential equations u(n)(t) + ~ AiU(i)(t) = 0, t ~ 0, {{ U(k)(O) = Uk, 0 ~ k ~ n-l. where AQ, Ab . . . , A - are linear operators in a topological vector space E. n 1 Many problems in nature can be modeled as (ACP ). For example, many n initial value or initial-boundary value problems for partial differential equations, stemmed from mechanics, physics, engineering, control theory, etc. , can be trans lated into this form by regarding the partial differential operators in the space variables as operators Ai (0 ~ i ~ n - 1) in some function space E and letting the boundary conditions (if any) be absorbed into the definition of the space E or of the domain of Ai (this idea of treating initial value or initial-boundary value problems was discovered independently by E. Hille and K. Yosida in the forties). The theory of (ACP ) is closely connected with many other branches of n mathematics. Therefore, the study of (ACPn) is important for both theoretical investigations and practical applications. Over the past half a century, (ACP ) has been studied extensively.
Physical Description:	1 online resource (xii, 300 pages).
Bibliography:	Includes bibliographical references (pages 269-297) and index.
ISBN:	9783540494799 3540494790 3540652388 9783540652380
ISSN:	0075-8434 ;