A. Bensoussan - Böcker

This is a reprinting of a book originally published in 1978. At that time it was the first book on the subject of homogenization, which is the asymptotic analysis of partial differential equations with rapidly oscillating coefficients, and as such it sets the stage for what problems to consider and what methods to use, including probabilistic methods. At the time the book was written the use of asymptotic expansions with multiple scales was new, especially their use as a theoretical tool, combined with energy methods and the construction of test functions for analysis with weak convergence methods. Before this book, multiple scale methods were primarily used for non-linear oscillation problems in the applied mathematics community, not for analyzing spatial oscillations as in homogenization. In the current printing a number of minor corrections have been made, and the bibliography was significantly expanded to include some of the most important recent references. This book gives systematic introduction of multiple scale methods for partial differential equations, including their original use for rigorous mathematical analysis in elliptic, parabolic, and hyperbolic problems, and with the use of probabilistic methods when appropriate. The book continues to be interesting and useful to readers of different backgrounds, both from pure and applied mathematics, because of its informal style of introducing the multiple scale methodology and the detailed proofs.

IRIA-LABORIA + has organized, this year, an International Conference on Control Theory, Numerical Methods and Computer Systems Modelling. This meeting which was sponsored by the International Federation for Information Proce s sing (IFIP) and by the European Institute for Advanced Studies in Management, took place in June (17-21) with the participation of more than 200 specialists among which 55 participants were repre senting 12 different countrie s. This volume of the Springer-Verlag Series "Lecture Notes" contains the lectures presented during the meeting and demonstrates the high interest of the research which is actually carried out in these fields. We specially wish to thank Monsieur DANZIN, Director of IRIA, for the interest he has shown for this Symposium, Professor BALAKRISHNAN who has arranged for IFIP to sponsor our meeting and Professor GRAVES, Director of the European Institute for Advanced Studies in Management for his support. The IRIA Public Relations has been of a great assistance to the Organization Committee and we wish to thank Mademoiselle BRICHETEAU and her staff for their contribution.At last we expre s s our gratitude to the Se s sions Chairmen and all the speakers for the very interesting discussions they have directed. A. BENSOUSSAN and J.L. LIONS +Institut de Recherche d'Informatique et d'Automatique Laboratoire de Recherche de l'IRIA PREFACE L'IRIA-LABORIA + a organise cette annee une Conference Internationale sur la Theorie du Contrale, les Methodes Nurneriques et la Modelisation des Systernes Informatiques.

INRIA, Institut National de Recherche en Informatique et en Automatique

INRIA, Institut National de Recherche en Informatique et en Automatique

From the foreword: "This volume contains most of the 113 papers presented during the Eighth International Conference on Analysis and Optimization of Systems organized by the Institut National de Recherche en Informatique et en Automatique. Papers were presented by speakers coming from 21 different countries. These papers deal with both theoretical and practical aspects of Analysis and Optimization of Systems. Most of the topics of System Theory have been covered and five invited speakers of international reputation have presented the new trends of the field."

Proceedings of the 9th International Conference held at Antibes in June 1990, on a variety of optimization issues.