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2017 Fiscal Year Final Research Report

Development of numerical analysis of blow-up phenomena - blow-up curve, regional blow-up, multiple blow-up -

Research Project

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Project/Area Number 15K13461
Research Category

Grant-in-Aid for Challenging Exploratory Research

Allocation TypeMulti-year Fund
Research Field Foundations of mathematics/Applied mathematics
Research InstitutionShibaura Institute of Technology

Principal Investigator

Ishiwata Tetsuya  芝浦工業大学, システム理工学部, 教授 (50334917)

Co-Investigator(Kenkyū-buntansha) 齊藤 宣一  東京大学, 大学院数理科学研究科, 教授 (00334706)
名和 範人  明治大学, 理工学部, 専任教授 (90218066)
佐々木 多希子  早稲田大学, グローバルエデュケーションセンター, 助手 (30780150)
Project Period (FY) 2015-04-01 – 2018-03-31
Keywords数値解析 / 解の爆発 / 爆発レート / 領域爆発 / 爆発曲線 / 再爆発現象
Outline of Final Research Achievements

Blow-up phenomena are typical nonlinear phenomena in several mathematical models. Here “blow-up” means that a size of the solution becomes infinity in a finite time, that is, the solution has a singularity. In this research project, we focus on blow-up curves, regional blow-up and multiple blow-up in some partial differential equations. In these phenomena it is important to understand the geometric properties of the solutions in time-space plane, the strength of the singularity(blow-up rate), and their relations. We show some numerical methods to these topics and get many numerical observations. Moreover, we show mathematical results on some of those numerical conjectures.

Free Research Field

応用数学

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Published: 2019-03-29  

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