Stability of solution and reconstruction in inverse problems

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This project aims at mathematical analysis and numerical analysis based on the mathematical analysis for inverse problems in applied sciences, Moreover we have studied related problems in applications, from the viewpoint of inverse problems, and prepared possible numerical methods.We conclude that by this project, we have established satisfactory theoretical results. Moreover, as for the development of numerical methods on the basis of the theoretical aspects, several methods have been proposed and tested for numerical examples. Still we have not compared the numerical results with real data directly from the real worlds such as works or plants. Therefore the continuation of this kind of projects are strongly demanded.For researches of related problems with inverse problems, the participants have achieved remarkable results by their own specialities.We have held several surveys concerning inverse problems by foreign researchers and taken part in international conferences on inverse problems for presenting the outputs of this project.With results obtained by this project, M. Yamamoto et al. have published a monograph on the mathematics and the numerical methods of inverse problems.Onishi, Tosaka, Iso, Kawarada, Miyoshi, Kimura, Ushijima and Kako have worked for inverse problems and related problems in applied sciences, from numerical points of view. Nakamura, Saitoh, Ikehata, Tanuma, Kubo have worked for theoretical aspects of inverse problems.