2012 Fiscal Year Final Research Report
Entropy solutions for nonlinear degenerate parabolic equations and hyperbolic systems of conservation laws
| Project/Area Number |
22540235
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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 | Waseda University |
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Principal Investigator |
KOBAYASI Kazuo 早稲田大学, 教育・総合科学学術院, 教授 (80103612)
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| Co-Investigator(Kenkyū-buntansha) |
OHWA Hiroki 新潟大学, 自然科学系, 助教 (10549158)
TAKAGI Satoru 早稲田大学, 付属研究所, 助教 (50367017)
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| Project Period (FY) |
2010 – 2012
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| Keywords | エントロピー解 / Kinetic 解 / 非線形退化放物型方程式 / リーマン問題 / 非線形保存型方程式 / 波面追跡法 / 関数方程式 |
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| Research Abstract |
The theory of the Cauchy problem for one-dimensinal n×n systems of conservation laws has evolved from a set of works by A. Bressan et al via the front tracking method. The argument developed there is, however, rather complex. In this research we restricted ourself to the case of one-dimensional 2×2 systems of conservation laws and succeeded to make clear the geometrical structure of shock curves for the Riemann problem (with initial data of step functions). Using the structure theory established here we gave a simple argument in the front trucking method and proved the existence of entropy solutions to general Cauchy problems. Besides, we obtained the comparison and existence of entropy solutions to nonlinear anisotropic degenerate parabolic equations with initial-boundary conditions.
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