Structure of the Solutions to Partial Differential Equations Degenerating on the Initial Surface
Project/Area Number  10640157 
Research Category 
GrantinAid for Scientific Research (C).

Section  一般 
Research Field 
Basic analysis

Research Institution  Osaka ElectroCommunication University 
Principal Investigator 
MANDAI Takeshi Osaka ElectroCommunication University, Faculty of Engineering, Professor, 工学部, 教授 (10181843)

CoInvestigator(Kenkyūbuntansha) 
SHIGA Kiyoshi Gifu University, Faculty of Engineering, Professor, 工学部, 教授 (10022683)
浅川 秀一 岐阜大学, 工学部, 助手 (00211003)
室 政和 岐阜大学, 工学部, 教授 (70127934)
TAHARA Hidetoshi Sophia University, Faculty of Science and Engineering, Professor, 理工学部, 教授 (60101028)
IGARI Katsuju Ehime University, Faculty of Engineering, Professor, 工学部, 教授 (90025487)
YAMAHARA Hideo Osaka ElectroCommunication University, Faculty of Engineering, Associate Professor, 工学部, 助教授 (30103344)
浅倉 史興 大阪電気通信大学, 工学部, 教授 (20140238)
SAKATA Sadahisa Osaka ElectroCommunication University, Faculty of Engineering, Associate Professor, 工学部, 助教授 (60175362)

Project Fiscal Year 
1998 – 1999

Project Status 
Completed(Fiscal Year 1999)

Budget Amount *help 
¥3,800,000 (Direct Cost : ¥3,800,000)
Fiscal Year 1999 : ¥1,900,000 (Direct Cost : ¥1,900,000)
Fiscal Year 1998 : ¥1,900,000 (Direct Cost : ¥1,900,000)

Keywords  Fuchsian partial differential equations / regular singularity / method of Frobenius / characteristic exponent / characteristic Cauchy problem / フックス型偏微分方程式 / 確定特異点 / フロベニウスの方法 / 特性指数 / 特性的初期値問題 / フックス型偏微分作用素 / ワックス型偏微分作用素 
Research Abstract 
The Indicial polynomial and its zero called characteristic exponent play an important role in the study of Fuchsian partial differential equations in the sense of BaouendiGoulaouic, that is, linear partial differential equations with regular singularity along the initial surface. Some conditions on the indicial polynomial have been assumed in most of the results. Mainly, we aimed to consider Fuchsian equations without any assumptions on the indicial polynomial. The main results are the following. First, we could construct a solution map which gives the local structure the solutions to homogeneous single Fuchsian partial differential equations in a complex domain. We also had a similar result for Fuchsian systems of homogeneous equations. We could also construct a solution to inhomogeneous Fuchsian equations, which is 'near' to a holomorphic solution. Our idea seems to be applicable to wider range of problems, and we have already some results of extensions.

Report
(4results)
Research Output
(3results)