| Project/Area Number |
25870005
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Mathematical analysis
Foundations of mathematics/Applied mathematics
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| Research Institution | Hokkaido University (2014-2015)
Tohoku University (2013) |
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Principal Investigator |
Nakano Naoto 北海道大学, 理学(系)研究科(研究院), 研究院研究員 (30612642)
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| Project Period (FY) |
2013-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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| Keywords | 偏微分方程式 / 常微分方程式 / 単純剪断流 / 特異定常解 / 数値解析 / 連続体モデル / 線型安定性 / 正則化方程式 |
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| Outline of Final Research Achievements |
This research project studied mathematical analysis and numerical analysis for a continuum model with density gradient-dependent stress. This model is represented by a system of partial differential equations for the density function and the velocity vector field of the continuum. Since the principal terms include degenerate non-linear terms with respect to the density, it is difficult to prove the well-posedness of, for example, an initial-boundary value problem for this model in general. We focused on a characteristic steady solution specific to this model, which is so called cycloid solution, to deepen understandings of characteristic properties of a continuum behaviour described by this model. Here, by performing mathematical and numerical analysis, we obtained some well-posedness results and resolved singular profiles of the solutions.
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