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  • © 1998

The Cauchy Problem for Higher Order Abstract Differential Equations

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

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Table of contents (7 chapters)

  1. Front Matter

    Pages N2-XII
  2. Wellposedness and solvability

    • Ti-Jun Xiao, Jin Liang
    Pages 45-83
  3. Generalized wellposedness

    • Ti-Jun Xiao, Jin Liang
    Pages 85-140
  4. Analyticity and parabolicity

    • Ti-Jun Xiao, Jin Liang
    Pages 141-176
  5. Exponential growth bound and exponential stability

    • Ti-Jun Xiao, Jin Liang
    Pages 177-197
  6. Differentiability and norm continuity

    • Ti-Jun Xiao, Jin Liang
    Pages 199-238
  7. Almost periodicity

    • Ti-Jun Xiao, Jin Liang
    Pages 239-261
  8. Back Matter

    Pages 263-309

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.

Keywords

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

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: Differential Equations

Buying options

eBook USD 49.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 65.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions