2003 Fiscal Year Final Research Report Summary
Research on the time global solutions for the partial differential equations of Kirchhoff type
| Project/Area Number |
14540188
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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 |
YAMAZAKI Taeko YAMAZAKI,Taeko, 理工学部, 助教授 (60220315)
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| Co-Investigator(Kenkyū-buntansha) |
TACHIKAWA Atsushi TACHIKAWA,Atsushi, 理工学部, 教授 (50188257)
OKA Satoshi OKA,Satoshi, 理工学部, 教授 (70120178)
KOBAYASHI Reido KOBAYASHI,Reido, 理工学部, 教授 (70120186)
USHIJIMA Takeo USHIJIMA,Takeo, 理工学部, 助教授 (30339113)
KOBAYASHI Takao KOBAYASHI,Takao, 理工学部, 教授 (90178319)
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| Project Period (FY) |
2002 – 2003
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| Keywords | Kirchhoff equations / global solvability / hyperbolic equations / dissipative term / forcing term / spectral decomposition / linear wave equations / decay estimate |
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| Research Abstract |
1.We studied the initial value problem for the dissipative hyperbolic equation of Kirchhoff type associated to a non-negative self-adjoint operator A in a Hilbert space, with a dissipative term and a forcing term.We gave sufficient conditions on the forcing term, related with the spectral decompo-sition of the operator A, for the global unique solvability of this initial value problem with small inital value.
2.We studied the unique global solvability of initial(boundary)value problem for the Kirchhoff equations in exterior domains or in the whole Euclidean space for dimension larger than three.The following sufficient condition is known: initial data is sufficiently small in some weighted Sobolev spaces for the whole space case ; the generalized Fourier transform of the initial data is sufficiently small in some weighted Sobolev spaces for the exterior domain case. We gave sufficient conditions on the usual Sobolev norm of the initial data, by showing that the global solvability for this equation follows from a time decay estimate of the solution of the linear wave equation.
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