Co-operative research of partial differential equations and its applications

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The subjects of this research were well achieved by meetings and discussions organized by each investigator and by a big meeting organized co-operatively by the whole investigators.The subjects of this project are mainly concerned with theory of partial differential equations, but, as a matter of course, the theory of ordinary differential equations has deep relationships with studies of Partial differential equations. Therefore, we have organized the meetings in co-operations with researchers of ordinary differential equations. Thus, naturally the results obtained by this project extend over the whole theory of differential equations.In the year of 1990, we organized mainly several middle size meetings, whose subjects were concentrated sharply in topics of central subjects of our project. Namely, we studied around Problems of hyperbolic equations, spectral and scattering theory, and elastic equation and hyperbolic problems appeared in engineering. In these meetings, very ardor discussions were exchanged and we have recognized the deep relations between different subjects. These meeting enable us to consider the various topics in partial differential equations in total. This permits us to treat the theory of partial differential equations as a non-separable subject, that is, in a global perspective of differential equations.In 1991 we organized a big meeting which covers all the fields of differential equations. By these researches we have recognized the variety of the theory of differential equations and generated many germs which will certainly give us many beautiful fruits of mathematics.