Abstract
The published literature related to distributed parameter systems theoryis quite large, and it is not feasible in a single book to give a detailedreview on the wide historical development of all of it. Our choice of whatto cover was motivated by the following consideration. Since distributedparameter systems evolve in time and space, the research investigationson their analysis and control focus on considering the whole system domainfor any study. We feel strongly that within this research field, animportant consideration was missing; that of considering that the systemmay give raise to prescribed subdomains (regions) where one has toachieve an objective. This is the case of so many applications rangingfrom engineering to life sciences. For that reason, covering classical prerequisitein analysis and control areas, we have devoted the book to theextension of the classical distributed parameter results to regional ones.Students of mathematics do not come into contacts with distributedparameter systems during their classes. They are introduced to themwhen they start research and often they are influenced by the knowledgeand the advice of experimented scientists. This was our case at the verybeginning of these research investigations in the mid 70’s. We would liketo express our special thanks to many of them and mainly late ProfessorAnthony J. Pritchard (University of Warwick, GB) and late Professor J.L. Lions (College de France) who were so encouraging in front of our determinationin driving an academic carrier. We also express our thanksto our co-workers and research students. We wish to acknowledge thefeedback from all those who took courses based on various parts of thisbook.This book may be used by graduate students in mathematics, engineering,physics, and even by students from other fields such as life orenvironmental sciences. This book may also be used as an informationvi Avant-propossource for researchers and education professionals. We assume that thereaders already know the basic concepts of analysis and control of distributedparameter systems.