SYSTEMS THEORY
Résumé
The published literature related to distributed parameter systems theory
is quite large, and it is not feasible in a single book to give a detailed
review on the wide historical development of all of it. Our choice of what
to cover was motivated by the following consideration. Since distributed
parameter systems evolve in time and space, the research investigations
on their analysis and control focus on considering the whole system domain
for any study. We feel strongly that within this research field, an
important consideration was missing; that of considering that the system
may give raise to prescribed subdomains (regions) where one has to
achieve an objective. This is the case of so many applications ranging
from engineering to life sciences. For that reason, covering classical prerequisite
in analysis and control areas, we have devoted the book to the
extension of the classical distributed parameter results to regional ones.
Students of mathematics do not come into contacts with distributed
parameter systems during their classes. They are introduced to them
when they start research and often they are influenced by the knowledge
and the advice of experimented scientists. This was our case at the very
beginning of these research investigations in the mid 70’s. We would like
to express our special thanks to many of them and mainly late Professor
Anthony J. Pritchard (University of Warwick, GB) and late Professor J.
L. Lions (College de France) who were so encouraging in front of our determination
in driving an academic carrier. We also express our thanks
to our co-workers and research students. We wish to acknowledge the
feedback from all those who took courses based on various parts of this
book.
This book may be used by graduate students in mathematics, engineering,
physics, and even by students from other fields such as life or
environmental sciences. This book may also be used as an information
vi Avant-propos
source for researchers and education professionals. We assume that the
readers already know the basic concepts of analysis and control of distributed
parameter systems.