2014 Fiscal Year Final Research Report
Study for hierarchical structure underlying between hyperbolicity and parabolicity
| Project/Area Number |
24654036
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Basic analysis
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| Research Institution | Waseda University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
OZAWA Tohru 早稲田大学, 理工学術院, 教授 (70204196)
NISHIHARA Kenji 早稲田大学, 政治経済学術院, 教授 (60141876)
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Keywords | 放物型方程式 / 双曲型方程式 / 発展方程式 / 平滑化現象 |
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| Outline of Final Research Achievements |
It is very important to pursue mathematical study for Partial Differential Equations which describe various phenomena arising in natural sciences such as Physics. However, since the behavior of solutions of wave equation, a typical example of hyperbolic equation, and heat equation, a typical example of parabolic equation, is quite different to each other, the method of study and the group of researchers are both separated. Based on the fact that wave equation with strong dissipation acquires some parabolicity which was detected by research representative, we studied some abstract hyperbolic equation with strong dissipation and clarified the mechanism of acquiring the parabolicity and revealed the hierarchical structure underlying between hyperbolicity and parabolicity.
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| Free Research Field |
非線形偏微分方程式
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