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)
