## 偏微分方程式セミナー（2014/10/20）：On the local smoothing for the Klein-Gordon equation, 久保英夫氏

2014年 　 10月 20日 16時 30分 ～ 2014年 　 10月 20日 17時 30分

In this talk, we study asymptotic behavior of a space-time norm, which is
localized in space, for solutions to the Klein-Gordon equation in the
energy class. More precisely, we compute a limit of the space-time norm
with respect to the localization parameter. This type of study has been
done for the Schrodinger equation and the wave equation by Prof. L.
Vega and Prof. N. Visciglia. In the case of the Klein-Gordon equation, the
limit is somehow intermediate between the Schrodinger case and the
wave case. Indeed, it shows different nature of the solution to the
Klein-Gordon equation according to the low frequency part and the high
frequency part.