2011 Fiscal Year Final Research Report
Asymptotic behavior and singular limit problem for dissipative hyperbolic equations
| Project/Area Number |
21540201
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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 |
Basic analysis
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| Research Institution | Tokyo University of Science |
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Principal Investigator |
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| Project Period (FY) |
2009 – 2011
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| Keywords | Kirchhhoff方程式 / 消散型双曲型方程式 |
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| Research Abstract |
We considered dissipative Kirchhoff equation with dissipation, where the coefficient of the dissipation decays with respect to the time valuable. First we consider dissipative Kirchhoff equation where the coefficient of the dissipation term depends time and space valuables and decays slowly than the critical exponent with respect to the time valuable. Then we proved the unique global existence of the solution for initial data with small Sobolev norm. Secondly we considered the dissipative Kirchhoff equation where the coefficient of the dissipation term depends only on time valuable which decays rapidly. Then we showed the unique global solvability and existence of the scattering on some class of the functions.
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