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The Cauchy problem for higher-order abstract differential equations

Author: Ti-Jun Xiao; Jin Liang
Publisher: Berlin ; New York : Springer, ©1998.
Series: Lecture notes in mathematics (Springer-Verlag), 1701.
Edition/Format:   eBook : Document : EnglishView all editions and formats
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Xiao, Ti-Jun, 1964-
Cauchy problem for higher-order abstract differential equations.
Berlin ; New York : Springer, ©1998
(DLC) 98047648
(OCoLC)40163507
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Ti-Jun Xiao; Jin Liang
ISBN: 9783540494799 3540494790
OCLC Number: 159958072
Description: 1 online resource (xii, 300 pages).
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.
Series Title: Lecture notes in mathematics (Springer-Verlag), 1701.
Responsibility: Ti-Jun Xiao, Jin Liang.

Abstract:

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  Read more...

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