2009 Fiscal Year Final Research Report
Structures and singular perturbations limits of solutions to the systems of non-strictly hyperbolic nonlinear partial differential equations for the conservation laws in the phase transition dynamics
| Project/Area Number |
18540202
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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 | International Christian University (2007-2009)
University of Tsukuba (2006) |
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Principal Investigator |
YAMAZAKI Mitsuru International Christian University, 教養学部, 教授 (30240732)
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| Co-Investigator(Kenkyū-buntansha) |
ISOZAKI Hiroshi 筑波大学, 数理物質科学研究科, 教授 (90111913)
ASAKURA Fumioki 大阪電気通信大学, 工学部, 教授 (20140238)
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| Project Period (FY) |
2006 – 2009
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| Keywords | 超局所解析 / 偏微分方程式 / 双曲型保存則系 / エントロピー / 流体力学 |
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| Research Abstract |
(1) We show that, for the 2×2 nonlinear hyperbolic systems of conservation laws with an umbilic point, there exists classical solutions, shock waves and also non-classical solutions, overcompressive shock waves. (2) We give a sufficient condition for guarantee that the singular perturbation limits of the hyperbolic conservation conservation equation with a higher order terms converge to the solution to the conservation law. (3) We prove the existence of solutions including vacuum to the relativistic Euler equation by using the compensated compactness method. (4) We show the stability of solution to the Boltzmann equation near vacuum in the context of general Lp spaces.
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