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The Cauchy Problem for Higher Order Abstract Differential Equations

  • Book
  • © 1998

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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1701)

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About this book

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.

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Keywords

Table of contents (7 chapters)

Authors and Affiliations

  • Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, People’s Republic of China

    Ti-Jun Xiao, Jin Liang

Bibliographic Information

  • Book Title: The Cauchy Problem for Higher Order Abstract Differential Equations

  • Authors: Ti-Jun Xiao, Jin Liang

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/978-3-540-49479-9

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1998

  • Softcover ISBN: 978-3-540-65238-0Published: 18 November 1998

  • eBook ISBN: 978-3-540-49479-9Published: 11 December 2013

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XIV, 300

  • Topics: Ordinary Differential Equations

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