Lecture Notes in Mathematics

The Cauchy Problem for Higher Order Abstract Differential Equations

Authors: Xiao, Ti-Jun, Liang, Jin

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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.

Table of contents (7 chapters)

  • Laplace transforms and operator families in locally convex spaces

    Xiao, Ti-Jun (et al.)

    Pages 1-44

  • Wellposedness and solvability

    Xiao, Ti-Jun (et al.)

    Pages 45-83

  • Generalized wellposedness

    Xiao, Ti-Jun (et al.)

    Pages 85-140

  • Analyticity and parabolicity

    Xiao, Ti-Jun (et al.)

    Pages 141-176

  • Exponential growth bound and exponential stability

    Xiao, Ti-Jun (et al.)

    Pages 177-197

Buy this book

eBook $49.99
price for USA (gross)
  • ISBN 978-3-540-49479-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $65.00
price for USA
  • ISBN 978-3-540-65238-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
The Cauchy Problem for Higher Order Abstract Differential Equations
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1701
Copyright
1998
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-49479-9
DOI
10.1007/978-3-540-49479-9
Softcover ISBN
978-3-540-65238-0
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XIV, 300
Topics