Preface -- Inverse Problems for Partial Differential Equations First Edition Preface

Abstract

This book describes the contemporary state of the theory and some numerical aspects of inverse problems in partial differential equations. The topic is of substantial and growing interest for many scientists and engineers and accordingly to graduate students in these areas. Mathematically, these problems are relatively new and quite challenging due to the lack of conventional stability and to nonlinearity and non-convexity. Applications include recovery of inclusions from anomalies of their gravitational fields; reconstruction of the interior of the human body from exterior electrical, ultrasonic, and magnetic measurements; recovery of interior structural parameters of detail of machines and of the underground from similar data (nondestructive evaluation); and locating flying or navigated objects from their acoustic or electromagnetic fields. Currently, there are hundreds of publications containing new and interesting results.