Co-operative research of partial differential equations and its applications

通过每位研究者组织的会议和讨论以及由全体研究者合作组织的大型会议，本研究的主题得到了很好的实现。本课题主要研究偏微分方程理论，当然，常微分方程理论与偏微分方程研究也有很深的联系。因此，我们与常微分方程的研究人员合作组织了会议。因此，这个项目得到的结果自然可以推广到整个微分方程理论。在1990年，我们主要组织了几次中等规模的会议，其主题集中在我们项目的中心主题上。即围绕工程中出现的双曲型方程、谱与散射理论、弹性方程和双曲型问题进行研究。在这些会议中，我们进行了非常热烈的讨论，我们认识到不同主题之间的深厚关系。这些会议使我们能够全面考虑偏微分方程中的各种主题。这允许我们把偏微分方程理论作为一个不可分离的学科来对待，也就是说，从微分方程的全局角度来看。1991年，我们组织了一个涵盖微分方程所有领域的大型会议。通过这些研究，我们认识到了微分方程理论的多样性，产生了许多细菌，这些细菌必将给我们带来许多美丽的数学果实。

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.