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The Cauchy Problem for Higher Order Abstract Differential Equations

  • Ti-Jun Xiao
  • Jin Liang

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

Table of contents

  1. Front Matter
    Pages N2-XII
  2. Ti-Jun Xiao, Jin Liang
    Pages 45-83
  3. Ti-Jun Xiao, Jin Liang
    Pages 85-140
  4. Ti-Jun Xiao, Jin Liang
    Pages 141-176
  5. Ti-Jun Xiao, Jin Liang
    Pages 177-197
  6. Ti-Jun Xiao, Jin Liang
    Pages 199-238
  7. Ti-Jun Xiao, Jin Liang
    Pages 239-261
  8. Back Matter
    Pages 263-309

About this book

Introduction

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.

Keywords

Abstract differential equations Cauchy problem differential equation differential operator differential operators fucntional analysis functional analysis linear operators locally convex space

Authors and affiliations

  • Ti-Jun Xiao
    • 1
  • Jin Liang
    • 1
  1. 1.Department of MathematicsUniversity of Science and Technology of ChinaHefei, AnhuiPeople’s Republic of China

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-49479-9
  • Copyright Information Springer-Verlag Berlin Heidelberg 1998
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-65238-0
  • Online ISBN 978-3-540-49479-9
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site