2010 Fiscal Year Final Research Report
Time global structure of solutions of nonlinear conservation law with viscosity and relaxation
| Project/Area Number |
19340037
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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 |
Global analysis
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| Research Institution | Osaka University |
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Principal Investigator |
MATSUMURA Akitaka Osaka University, 大学院・情報科学研究科, 教授 (60115938)
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| Co-Investigator(Kenkyū-buntansha) |
CHAWANYA Takeshi 大阪大学, 大学院・情報科学研究科, 准教授 (80294148)
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| Co-Investigator(Renkei-kenkyūsha) |
ODANAKA Shinji 大阪大学, サイバーメディアセンター, 教授 (20324858)
NISHIHARA Kenji 早稲田大学, 政治経済学部, 教授 (60141876)
NISHIBATA Shinya 東京工業大学, 大学院・情報理工学研究科, 教授 (80279299)
YANAGISAWA Taku 奈良女子大学, 大学院・自然科学研究科, 教授 (30192389)
KOMATSU Gen 大阪大学, 大学院・理学研究科, 准教授 (60108446)
TSUGE Naoki 岐阜大学, 教育学部, 准教授 (30449897)
IOHARA Takao 大阪大学, 大学院・理学研究科, 助教 (00294140)
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| Project Period (FY) |
2007 – 2010
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| Keywords | 保存則 / 時間大域解 / 長時間挙動 / ナヴィエ・ストークス方程式 / 半導体方程式 |
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| Research Abstract |
Several new weighted energy methods were successfully proposed to have a priori estimates of solutions. With the aid of these methods, has been much progressed the analysis on the large time behaviors of the solutions of scalar viscous conservation law with non-convex flux, system of equations of viscous ideal gas, dissipative wave equations, etc. Also for model equations of semiconductor, the analysis on existence, uniqueness and asymptotic stability of stationary solutions, hierarchy structures with respect to several physical parameters, and methods of numerical computation has been much progressed.
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