2011 Fiscal Year Final Research Report
On the study of the lifespan for nonlinear hyperbolic systems
| Project/Area Number |
20540202
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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 | University of Tsukuba |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
KAJITANI Kunihiko 筑波大学, 名誉教授 (00026262)
ISHIWATA Satoshi 筑波大学, 数理物質系, 助教 (70375393)
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| Co-Investigator(Renkei-kenkyūsha) |
HIROSAWA Fumihiko 山口大学, 大学院・理工学研究科, 准教授 (50364732)
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| Project Period (FY) |
2008 – 2011
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| Keywords | 関数方程式論 / 双曲型システム / ライフスパン |
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| Research Abstract |
We have succeeded to obtain the results concerned with well-posedness and ill-posedness of the Cauchy problem for hyperbolic equations and systems with coefficients depending on the time variable. The well-posedness means that the life span tends to infinity, and the ill-posedness means that the solution blows up in a finite life span. In particular, we have also succeeded to get a representation formula of the solution (which possibly shows the exact value of the life span) and a construction of the approximate solution (which can be expected to give the order of the life span ).
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