Research on propagation of singularities for nonlinear wave equations
| Project/Area Number |
14540215
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Global analysis
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| Research Institution | TOKYO UNIVERSITY OF SCIENCE |
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Principal Investigator |
KATO Keiichi Tokyo University of Science, Associate Professor, 理学部第一部, 助教授 (50224499)
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| Co-Investigator(Kenkyū-buntansha) |
KOMATSU Hikosaburo Tokyo University of Science, Professor, 理学部第一部, 教授 (40011473)
OGAWA Takayoshi Tohoku University, Professor, 大学院・理学研究科, 教授 (20224107)
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| Project Period (FY) |
2002 – 2004
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| Project Status |
Completed (Fiscal Year 2004)
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| Budget Amount *help |
¥3,300,000 (Direct Cost: ¥3,300,000)
Fiscal Year 2004: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2003: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2002: ¥1,300,000 (Direct Cost: ¥1,300,000)
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| Keywords | nonlinear wave equation / propagation of singularity / Benjamin-Ono equation / analyticity / wellposedness / 非線形偏微分方程式 / Fourier Restriction / 特異性伝播 / KdV方程式 / Fourier ristriction / 非線形Schrodinger方程式 |
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| Research Abstract |
1.The head investigator and co-investigator T.Ogawa has studied on the sufficient condition for solutions to the Benjamin-Ono equation to be analytic in space and time variables for t>0 with E.Kaikina and P.I.Naumkin. Under the condition that initial data have some singularity at the origin, we show that the solution is analytic for t>0.
2.We have investigated the existence of solutions for the initial value problem of the Benjamin-Ono equation. However it is impossible to apply Picard's iteration method to the Benjamin-Ono equation in usual Sobolev space, we show that Picard's iteration method is applicable for some Sobolev space with homogeneous and inhomogeneous multipliers.
3.We have investigate the propagation of singularities for the nonlinear wave equations with nonlinear term satisfying null condition. Regularity estimate can be improved under the null condition for nonlinear term.
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Report
(4 results)
Research Products
(3 results)
