Modern Birkhäuser Classics

Evolutionary Integral Equations and Applications

Authors: Prüss, Jan

  • Presents a general approach to linear evolutionary systems 
  • Clearly written and of lasting value 
  • A substantial part of the results presented originate from the author​
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  • ISBN 978-3-0348-0499-8
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About this book

This book deals with evolutionary systems whose equation of state can be formulated as a linear Volterra equation in a Banach space. The main feature of the kernels involved is that they consist of unbounded linear operators. The aim is a coherent presentation of the state of art of the theory including detailed proofs and its applications to problems from mathematical physics, such as viscoelasticity, heat conduction, and electrodynamics with memory. The importance of evolutionary integral equations ‒ which form a larger class than do evolution equations​ ‒ stems from such applications and therefore special emphasis is placed on these. A number of models are derived and, by means of the developed theory, discussed thoroughly. An annotated bibliography containing 450 entries increases the book’s value as an incisive reference text. --- This excellent book presents a general approach to linear evolutionary systems, with an emphasis on infinite-dimensional systems with time delays, such as those occurring in linear viscoelasticity with or without thermal effects. It gives a very natural and mature extension of the usual semigroup approach to a more general class of infinite-dimensional evolutionary systems. This is the first appearance in the form of a monograph of this recently developed theory. A substantial part of the results are due to the author, or are even new. (…) It is not a book that one reads in a few days. Rather, it should be considered as an investment with lasting value. (Zentralblatt MATH) In this book, the author, who has been at the forefront of research on these problems for the last decade, has collected, and in many places extended, the known theory for these equations. In addition, he has provided a framework that allows one to relate and evaluate diverse results in the literature. (Mathematical Reviews) This book constitutes a highly valuable addition to the existing literature on the theory of Volterra (evolutionary) integral equations and their applications in physics and engineering. (…) and for the first time the stress is on the infinite-dimensional case. (SIAM Reviews)

About the authors

Jan Prüss is a Professor of Mathematics at the Martin-Luther-Universität Halle-Wittenberg, Germany.

Table of contents (13 chapters)

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-3-0348-0499-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $99.00
price for USA
  • ISBN 978-3-0348-0498-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Evolutionary Integral Equations and Applications
Authors
Series Title
Modern Birkhäuser Classics
Copyright
2012
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel
eBook ISBN
978-3-0348-0499-8
DOI
10.1007/978-3-0348-0499-8
Softcover ISBN
978-3-0348-0498-1
Series ISSN
2197-1803
Edition Number
1
Number of Pages
XXVI, 366
Number of Illustrations and Tables
8 b/w illustrations
Additional Information
Originally published as volume 87 in the Monographs in Mathematics series
Topics