Scattering theory of partial differential equations and its applications

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Using this grand-in-aid, we organized seberal conferences of small size and of middle size. We studied the theory of partial differential equation, theoretically and concret problems in our daily life. The investigators shared the fields of problems and all the participants co-operated in integrating the researchs by organized by investigators.As we wrote in the above, we aimed to develope study of problems of partial differential equation in our daily life, and forcused the study to the inverse problems of partial differential equations, and developed the theoretial approach to these problems. Concerning the inverse problems, we experienced Kobe great earthquake during the period of our research. In fact, one of our main problem of research is a theoretical study of the inverse problem for the elastic wave, that is, the problem to determine the state of earth from the observation of the wave of earthquake. Even though Japan is a country of many earthquake, there are very few researcher in Mathematics. We have to develope the study of this inverse problems. Needless to say, we have to co-operate earth scientists, but we have to multiply the number of mathematicians interested in various problems related to earthquake.