GUEST EDITORS' INTRODUCTION

Abstract

This special section of Inverse Problems contains a selection of contributions to Picof'98, a conference on Inverse Problems, Control and Shape Optimization which took place in Carthage, Tunisia, 8 - 10 April 1998, at the Beit El Hikma Palace, the home of the Tunisian Academy of Science and Arts. During the conference the participants discussed the latest developments in the theoretical analysis and numerical methods for inverse, control and shape optimization problems. Picof'98 provided a forum for scientists and engineers to exchange ideas and share practical experience in this exciting domain which has many applications. The siting of this conference was evidence that today Tunisia plays an active part in the development of modern science and technology. The choice of Carthage, a place rich in history and a crossroads of many civilizations, was no accident. Indeed, the founding of Carthage was the subject of one of the oldest shape optimization problems: Dido's problem. In this section the reader will find a collection of 13 refereed papers from speakers at Picof'98. They cover a large spectrum of topics related to inverse problems and they can be sorted into four groups. The first group is devoted to identifiability questions arising in inverse problems for parabolic equations and comprises the papers of Isakov, and El Badia. The second group deals with the estimation of parameters in various models (flows in porous media, corrosion, structural design, etc), including upscaling and regularization techniques. This group contains the papers of Ewing et al, Chavent et al, Fasino and Inglese, and Ladevèze and Chouaki. The third group contains papers concerned with the reconstruction of defects such as cracks or obstacles, using algorithms based on the reciprocity gap principle, on the location of poles of meromorphic functions, or on inverse scattering approaches. This group contains the papers of Andrieux et al, Ben Abda et al, Baratchart et al, Alves and Ha-Duong, and Litman and Lesselier. The papers of Dziri and Zolésio, and Sokolowski and Zochowski concern shape optimization problems and techniques such as topological derivatives used to solve them, and these make up the fourth group. We hope that these papers will provide valuable reading for further research. We would like to thank Inverse Problems for publishing this selection of papers, all the authors for their contributions, and the referees for their comments and guidance, who together made this collection such a successful one. Furthermore we extend our gratitude to all those who made this conference possible by supporting its organization, and especially the Institut Français de Coopération de l'Ambassade de France en Tunisie which provided the financial support for this special section.