2012 Fiscal Year Final Research Report
Analysis of properties of solutions to dispersive equations via canonical transforms and comparison principle
| Project/Area Number |
20340029
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Nagoya University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
TSUGAWA Kotaro 名古屋大学, 大学院・多元数理科学研究科, 准教授 (70402451)
KATO Jun 名古屋大学, 大学院・多元数理科学研究科, 准教授 (00432237)
HISHIDA Toshiaki 名古屋大学, 大学院・多元数理科学研究科, 教授 (60257243)
MIYAKE Masatake 名古屋大学, 大学院・多元数理科学研究科, 教授 (70019496)
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| Co-Investigator(Renkei-kenkyūsha) |
TACHIZAWA Kazuya 北海道大学, 大学院・理学研究院, 准教授 (80227090)
TOMITA Naohito 大阪大学, 大学院・理学研究院, 准教授 (10437337)
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| Project Period (FY) |
2008 – 2012
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| Keywords | 正準変換 / 比較原理 / 分散型方程式 / 時空間評価 |
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| Research Abstract |
By developing a global boundedness theory of Fourier integral operators, we established a method to deduce estimates for solutions to partial differential equations from those for their normal forms, and furthermore, prepared a new method to make a comparison of estimates for solutions from the comparison of symbols of two partial differential equations, so that we approached to nonlinear problems.
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