A study Research of mathematical analysis and numerical analytical a non-linear continuum with density gradient-dependent stress

2015 Fiscal Year Final Research Report

• Project/Area Number: 25870005
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Mathematical analysis; Foundations of mathematics/Applied mathematics
• Research Institution: Hokkaido University (2014-2015); Tohoku University (2013)
• 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)
• Project Period (FY): 2013-04-01 – 2016-03-31
• 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

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.

Free Research Field

非線形解析