| Project/Area Number |
17K05338
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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 | Tokyo University of Science |
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Principal Investigator |
Yamazaki Taeko 東京理科大学, 理工学部数学科, 教授 (60220315)
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| Project Period (FY) |
2017-04-01 – 2021-03-31
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| Project Status |
Completed (Fiscal Year 2020)
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| Budget Amount *help |
¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2019: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2018: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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| Keywords | 消散型波動方程式 / 微分喪失型消散波動方程式 / 拡散現象 / structural dampping / structural damping / 解の漸近形 / 大域解の存在 / 解析学 |
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| Outline of Final Research Achievements |
It is known that solutions of linear wave equation with constant dissipation tend to solutions of corresponding parabolic equation, which is called diffusion phenomenon.Asymptotic behavior of solutions of wave equation with dissipative term of variable coefficients, depend on decay order of coefficient. On this research, we showed diffusion phenomenon of semilinear wave equation with constant structural dissipation and dissipative wave equation with time dependent coefficients of principal part and dissipative term. On the other hand, we showed continuity of wave operator and scattering operator on quasilinear dissipative wave equation of Kirchhoff type. Especially in the case that the coefficient of dissipative term is monotone decreasing, we obtained necessary and sufficient condition for the solution to be asymptotically free.
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| Academic Significance and Societal Importance of the Research Achievements |
消散項が周波数の分数冪に依存する構造的消散項をもつ波動方程式に関する大域解の一意存在性に関して先行研究で置かれていた冪と空間次元の関係に対する制限を外したことにより，統一的な結果を得ることができた．主部及び消散項が変数係数の場合についての拡散現象を示したことは，今後準線形方程式にも応用できることが見込まれる．また，Kichhoff型準線型波動方程式の漸近自由となるための必要十分条件が線形方程式と異なることを示すことにより，半線形と準線形の違いを明確にした．
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