On the lifespan and asymptotic behavior of solutions to systems of wave equations with nonlinear terms of long range effects
| Project/Area Number |
15K04955
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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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| Research Field |
Mathematical analysis
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| Research Institution | Mie University |
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Principal Investigator |
HIDANO KUNIO 三重大学, 教育学部, 教授 (00285090)
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| Co-Investigator(Kenkyū-buntansha) |
横山 和義 北海道科学大学, 工学部, 准教授 (20316243)
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | nonlinear wave equations / weak null condition / half wave equation / 初期値問題 / 適切性 / Strichartz型評価式 / 分数階微分 / chain rule / null condition / 波動方程式 / 時間大域解 / 最大存在時間 / 退化条件 / wave equation / lifespan / global solution |
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| Outline of Final Research Achievements |
In 2003, Lindblad and Rodnianski conjectured that the Cauchy problem for nonlinear wave equations satisfying the weak null condition would admit global (in time) solutions for small and smooth data. Using the ghost weight method due to Alinhac, we have studied the Cauchy problem for a system of quasi-linear wave equations satisfying this condition and proved that it admits global solutions for small and smooth data. Our result will be one of the basic steps toward the resolution of their conjecture.
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Report
(4 results)
Research Products
(24 results)
