Smoothing effect of Partial differential equations

在系数取决于时间和地点的情况下，平滑效果的问题被认为在技术上是非常困难的。在本研究中，我们可以找到新的方法来克服这个困难，并能够处理更一般的色散方程。本研究的结果已在日本学术讨论会和国际会议上发表，特别是能够证明一般色散方程的解析光滑效应，是一个重大的进展。

In the case of coefficients depending on time and places the problem of smoothing effect was considered to be very difficult technically. In this study we can find the new method to overcome this difficulty and are able to treat the more general dispersion equations. The results obtained in this study was published in the symposiums in Japan and in the international conference.In particular it is a great progress to be able to prove the analytically smoothing effect of general dispersion equations.