2001 Fiscal Year Final Research Report Summary
Study on the fundamental solutions to the equations of radiating gases and its applications
| Project/Area Number |
11440049
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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 |
KAWASHIMA Shuichi Kyushu. Univ., Grad. Sch. Math., Prof., 大学院・数理学研究院, 教授 (70144631)
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| Co-Investigator(Kenkyū-buntansha) |
OGAWA Takayoshi Kyushu. Univ., Grad. Sch. Math., Associate Prof., 大学院・数理学研究院, 助教授 (20224107)
KAGEI Yoshiyuki Kyushu. Univ., Grad. Sch. Math., Associate Prof., 大学院・数理学研究院, 助教授 (80243913)
YOSHIKAWA Atsushi Kyushu. Univ., Grad. Sch. Math., Prof., 大学院・数理学研究院, 教授 (80001866)
KOBAYASHI Takayuki Kyushu Ins. Tech., Fac. Eng., Associate Prof., 工学部, 助教授 (50272133)
NISHIBATA Shinya Tokyo Ins. Tech., Grad. Sch. Inf. Sci. Eng., Associate Prof., 大学院・情報理工学研究科, 助教授 (80279299)
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| Project Period (FY) |
1999 – 2001
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| Keywords | hyperbolic-elliptic system / hyperbolic-parabolic system / fundamental solution / pointwise estimate / global solutions / asymptotic slability / nonlinear waves / singular limit |
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| Research Abstract |
We study the stability of nonlinear waves for hyperbolic-elliptic coupled systems in radiation hydrodynamics and related equations.
1. By using the Fourier transform, we give a representation formula for the fundamental solutions to the linearized systems of hyperbolic-elliptic coupled systems and verify that the principal part of the fundamental solutions is given explicitly in terms of the heat kernel. Also, we obtain the sharp pointwise estimates for the error terms.
2. We obtain the pointwise decay estimate of solutions to the hyperbolic-elliptic coupled systems by using the representation formula for the fundamental solution and the corresponding estimates. Furthermore, we prove that the solution is asymptotic to the superposition of diffusion waves which propagate with the corresponding characteristic speeds.
3. We discuss a singular limit of the hyperbolic-elliptic coupled systems. We prove that at this limit, the solution of the hyperbolic-elliptic coupled system converges to that of the corresponding hyperbolic-parabolic coupled system.
4. We show the existence of stationary solutions to the discrete Boltzmann equation in the half space. It is proved that the stationary solution approaches the far field exponentially and is asymptotically stable for large time.
5. We study the asymptotic behavior of nonlinear waves for the isentropic Navier-Stokes equation in the half space. For the out-flow problem, we prove the asymptotic stability of nonlinear waves such as (1)stationary wave, (2)rarefaction wave, and (3)superposition of stationary wave and rarefaction wave.
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Research Products
(12 results)
