| Project/Area Number |
01540151
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
解析学
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| Research Institution | University of Osaka Prefecture |
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Principal Investigator |
TANIGUCHI Kazuo Instructor, 総合科学部, 講師 (80079037)
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| Co-Investigator(Kenkyū-buntansha) |
TOZAKI Yoshiharu Assistant, 総合科学部, 助手 (70079036)
SHINKAI Kenzo Professor, 総合科学部, 教授 (50079034)
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| Project Period (FY) |
1989 – 1990
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| Project Status |
Completed (Fiscal Year 1990)
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| Budget Amount *help |
¥1,600,000 (Direct Cost: ¥1,600,000)
Fiscal Year 1990: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 1989: ¥800,000 (Direct Cost: ¥800,000)
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| Keywords | hyperbolic equation / ultra wave front set / Gevrey class / propagation of singularity / Cauchy problem / Fourier integral operator / complex phase function / pourus media equation / フ-リエ積分作用素 / ジェヴレイ関数 / 波面集合 / 擬微分作用素 |
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| Research Abstract |
The fundamental solution of the Cauchy problem for a hyperbolic operator is given in the form of Fourier integral operator. As shown below, when the problem is not C^* well-posed, the symbol of the fundamental solution has exponential growth, that is, it is estimated not only from above but also from below by (1) <numerical formula> The constant kappa in (1) corresponds to the constant in the necessary and sufficient condition for the well-posedness in Gevrey classes. In order to study this phenomenon we define UWF^<(mu)>(u) (ultra wave front sets) for u that belongs to the space of ultradist
ributions S{kappa}' by <numerical formula> where X * S{kappa}*C^*_ and xi belongs to a conic neighborhood of xi_<omicron>. Then by using UWF^<(mu)>(u) we can state the propagation of very high singularities for the solution of not C^* well-posed Cauchy problem. We also construct the ndamental solutions of the Cauchy problem for degenerate hyperbolic operators (2) <numerical formula> (3) <numerical formula> with an even integer j and we investigated other related topics.
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