| Project/Area Number |
14540200
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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 | Tokyo Institute of Technology |
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Principal Investigator |
NISHIBATA Shinya Tokyo Institute of Technology, Graduate School of Information Science and Engineering, Associate Professor, 大学院・情報理工学研究科, 助教授 (80279299)
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| Co-Investigator(Kenkyū-buntansha) |
NISHIHARA Kenji Waseda University, School of Political Science and Economics, Professor, 政治経済学部, 教授 (60141876)
IGUCHI Tatsuo Tokyo Institute of Technology, Graduate School of Science and Engineering, Associate Professor, 大学院・総合理工学研究科, 助教授 (20294879)
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| Project Period (FY) |
2002 – 2004
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| Project Status |
Completed (Fiscal Year 2004)
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| Budget Amount *help |
¥4,000,000 (Direct Cost: ¥4,000,000)
Fiscal Year 2004: ¥1,400,000 (Direct Cost: ¥1,400,000)
Fiscal Year 2003: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2002: ¥1,600,000 (Direct Cost: ¥1,600,000)
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| Keywords | Viscous Conservation law / Asymptotic behavior / Compressible Naviei-Stokes equation / Nonlinear wave / Shock wave / Traveling wave / Rarefaction wave / Boundary layer |
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| Research Abstract |
This research project have aimed for the analysis on large-time behaviors of nonlinear waves to equations for the viscous gas, and viscous conservation laws over multi-dimensional half space. In 2002, we showed that the asymptotic behaviors of solutions to the multidimensional viscous conservation laws are classified into a rarefaction waves, stationary waves, and their superposition. This classification is same as for the 1-dimensional viscous conservation laws. Furthermore, we obtained convergence rates of solutions toward these non-linear waves for all possible cases subject to the spatial decay rates of the initial perturbation. Then in 2003, we tried to expand these results to the equations more meaningful from the physical point of views. We made the analysis on spherically symmetric flows for the compressible viscous Navier-Stokes equations in the exterior domain outside of a unit sphere over multidimensional space. The first result is that if the spatial dimension is greater th
… More
an or equal to 2, the isentropic model with potential external forces has a stationary solution, which is proved to be time asymptotically stable. Immediately after obtaining this result, we showed that the same result holds for the heat-conductive model if the spatial dimension is greater than or equal to 3. Here, let us note that in these theorems the small ness assumptions on neither the initial perturbations nor the external forces are necessary if the external force is attractive to the center of the sphere. Then in the research in 2004, we have obtained the convergence rate of solutions towards the stationary solutions for the 1-dimensional isentropic model subject to the initial perturbation. This theorem holds for both of the transonic and super sonic waves. After that the same result is proved for the heat-conductive gas for the super sonic flow. Right now, we are trying to expand these results to the multi-dimensional problem and have already obtained several results. For example, we have obtained the decay rate for the isentropic supersonic flow. Although the fiscal year 2004 is the end of this research project, I am still pursuing my researches on this research project Less
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