A study of solutions of systems of higher order partial differential equations by algebraic analysis methods and formula manipulation methods

2017 Fiscal Year Final Research Report

• Project/Area Number: 26400110
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: The University of Tokyo
• Principal Investigator: Kataoka Kiyoomi 東京大学, 大学院数理科学研究科, 名誉教授 (60107688)
• Project Period (FY): 2014-04-01 – 2018-03-31
• Keywords: 解析関数 / 偏微分方程式系 / 初期値・境界値混合問題 / D-加群 / 佐藤超関数 / 層のマイクロ台 / 一般化固有関数 / 蔵本モデル

Outline of Final Research Achievements

Concerning systems of linear analytic partial differential equations, we succeeded in giving coordinate-free formulations of the initial-boundary value mixed problems for D_X modules. At the same time we obtained a key theorem on the estimate of micro-supports of some holomorphic solution sheaf complexes in the sense of M.Kashiwara-P.Schapira, which is an essential tool clarifying the propagation of micro-analyticity of Sato hyperfunction solutions along the boundary. Concerning non-linear differential equations, we succeeded in clarifying the generalized eigenfunction expansions due to Hayato Chiba's theory on Kuramoto's weakly coupled many oscillators model on a circle for resonance phenomena. We found some essential error in Chiba's theory and gave a correct formulation and a proof.

Free Research Field

代数解析学