2023 Fiscal Year Final Research Report
The effect of scale factor on nonlinear waves in the expanding universe model
| Project/Area Number |
18K03351
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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 | Hirosaki University |
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Principal Investigator |
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| Project Period (FY) |
2018-04-01 – 2024-03-31
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| Keywords | 波動方程式 / 時間大域解存在 / 爆発解 / 解の存在時間 / スケール因子 / 膨張宇宙 |
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| Outline of Final Research Achievements |
We study nonlinear waves in the Friedmann-Lemaitre-Robertson-Walker spacetime, known as the standard cosmological model. The aim of this study is to elucidate the effect of the scale factor, representing the expansion rate of the universe, on nonlinear waves by comparing with known results in flat spacetime, such as the Minkowski spacetime. We classify the expanding universe model into decelerating, constant,and accelerating cases, and determine the global existence conditions, blow-up conditions, and estimates for the lifespan of blow-up solutions of the nonlinear wave equation. As a result, it is revealed that blow-up of solutions is more likely to occur compared to the Minkowski spacetime case, and furthermore, the lifespan of blow-up solutions is shorter.
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| Free Research Field |
偏微分方程式論
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| Academic Significance and Societal Importance of the Research Achievements |
標準宇宙モデルとして重要なフリードマン・ルメートル・ロバートソン・ウォーカー時空を背景時空とした非線形波動方程式を解析した結果，このような膨張宇宙モデルでは，平坦なミンコフスキー時空と比べ，非線形波動の特異性の発生が起こりやすいことを数学的解析により明らかにした．つまり，膨張宇宙モデルにおいては膨張速度が波動の挙動に大きな影響を及ぼしているということがわかった．今後の非線形波動方程式研究を進めるための指針を提供した．
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