Mathematical analysis based on the new stability condition for dissipative systems of partial differential equations
| Project/Area Number |
18K03369
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Review Section |
Basic Section 12020:Mathematical analysis-related
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| Research Institution | Kobe University |
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Principal Investigator |
Ueda Yoshihiro 神戸大学, 海事科学研究科, 准教授 (50534856)
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| Project Period (FY) |
2018-04-01 – 2023-03-31
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| Project Status |
Completed (Fiscal Year 2022)
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| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2020: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2019: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2018: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | 安定性解析 / 可微分性の損失 / 偏微分方程式論 / 漸近挙動 |
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| Outline of Final Research Achievements |
The main purpose of this research is mathematical analysis of differential equations arising in gas dynamics and elastodynamics. Especially, we focus on the stability theory for general systems of equations such as symmetric hyperbolic systems and hyperbolic-parabolic systems. As an example, I am studying the Euler-Maxwell, Plate, and Timoshenko systems as physical models. In particular, I am deeply analyzing a phenomenon called "regularity-loss" that appears when considering systems in which each term affects each other in a complex manner, and I am conducting research on linear stability analysis around equilibrium points.
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| Academic Significance and Societal Importance of the Research Achievements |
本研究は，偏微分方程式系に現れる消散効果が及ぼす解への影響を体系的に捉える点に最大の独自性と創造性がある．様々な物理現象が消散構造を持つ微分方程式系を用いてモデル化されているが，それぞれの物理モデルに関する解析は行われているものの，消散効果に焦点を置くことで一般化を試みているものは少ない．更に，本研究は消散行列に対称性を課さないより一般的な状況を考察しており，このような解析を行った結果はほぼ皆無である．これらの状況のもと，研究業績である一般論の構築によって，双曲型方程式系で表される物理モデルの安定性解析は全て同一手順により行われることとなり，数学的にも物理的にも非常に意義のある結果といえる．
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Report
(6 results)
Research Products
(62 results)
