| Project/Area Number |
13440049
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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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 | KYUSHU UNIVERSITY |
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Principal Investigator |
NAKAO Mitsuhiro Kyushu Univetrsity, Graduate School of Mathematics, Professor, 大学院・数理学研究院, 教授 (10037278)
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| Co-Investigator(Kenkyū-buntansha) |
KAWASHIMA Syuichi Kyushu University, Graduate School of Mathematics, Professer, 大学院・数理学研究院, 教授 (70144631)
SHIBATA Yoshihiro Waseda University, Facultry of Science and Technology, Professor, 理工学部, 教授 (50114088)
OGAWA Takayoshi Tohoku University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (20224107)
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| Project Period (FY) |
2001 – 2004
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| Project Status |
Completed (Fiscal Year 2004)
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| Budget Amount *help |
¥11,400,000 (Direct Cost: ¥11,400,000)
Fiscal Year 2004: ¥2,700,000 (Direct Cost: ¥2,700,000)
Fiscal Year 2003: ¥2,800,000 (Direct Cost: ¥2,800,000)
Fiscal Year 2002: ¥2,800,000 (Direct Cost: ¥2,800,000)
Fiscal Year 2001: ¥3,100,000 (Direct Cost: ¥3,100,000)
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| Keywords | Nonlinear wave eqations / Exterior problem / Energy decay / Global solutions / 局在非線形的摩擦項 / 波動方程式 / 周期解 / 局在的摩擦項 / 大域解 |
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| Research Abstract |
The main purpose of this research is concerned with the exterior problem for the quasi-linear wave equations. For this problem we have been successful in proving the global existence of smooth solutions under the effect of localized dissipation. We have achieved the results through two ways; one is based on the local energy decay and L^p estimates of solutions for linear equation, and the other one is the method to utilize total energy decay for the llinearized equation. Both ways are intended to make the effects of dissipation as weaker as possible, but, we have made no geometrical conditions on the shape of the boundary.
Concerning another problem on the energy decay for the equation with nonlinear dissipations we introduced anew concept ‘Half linear' and has been successful in deriving very delicate decay estimates of energy and applied them to the existence of global solutions for the equations with a nonlinear source term.
As related problems we have considered the existence and stability of periodic solutions for the nonlinear wave equations in bounded domains with some nonlinear localized dissipations. Further, we have considered the Kirchhoff type nonlinear wave equations in exterior domains. Under a nonlinear dissipations we have proved various results on global solutions. For the wave equation in exterior domains with a Neumann type boundary dissipation we have derived a new energy decay estimate.
Investigator Kawashima has derived many interesting results concerning Boltzman equations and hyperbolic conservation equations. Investigator Shibata has derived by the method of spectral analysis, many interesting results concerning the exterior problem for the compressive Navier-Stokes equations. Investigator Ogawa has proved precise estimates of solutions concerning behaviors and regularities of solutions for the nonlinear wave equations, nonlinear Shroadinger equations and some harmonic evolution equation.
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