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2017 Fiscal Year Final Research Report

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

Research Project

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Project/Area Number 26400110
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Basic analysis
Research InstitutionThe 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

URL: 

Published: 2019-03-29  

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