| Project/Area Number |
21540173
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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 |
Basic analysis
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| Research Institution | Nagoya Institute of Technology |
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Principal Investigator |
KUBO Masahiro 名古屋工業大学, 工学(系)研究科(研究院), 教授 (80205129)
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| Co-Investigator(Renkei-kenkyūsha) |
YAMAZAKI Noriaki 神奈川大学, 工学部, 教授 (90333658)
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| Project Period (FY) |
2009-04-01 – 2014-03-31
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | 非線形解析 / 非線形偏微分方程式 / 非線形発展方程式 / 変分不等式 / 凸解析 / 変分解析 / 特異摂動 / 劣微分作用素 / 準変分不等式 / 数理モデル解析 / Cahn-Hilliard方程式 / 変分原理 / 相転移モデル / 浸透流モデル |
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| Research Abstract |
Since Newton's invention, differential equations, that are equations containing unknown functions and their derivatives, have been and remain the most useful tool to describe and study mathematically various phenomina arising in physics and engineerings. From the viewpoint of abstract nonlinear evolution equations, we considered variational inequalities, that are problems of differential equations with constrains given by inequalities and imposed upon the unknown functions, and proved the existence of the singular limit of a problem containing a parameter whose limit changes the type of equation. Also in the course of the study, we proposed the concept of quasi-variational analysis by synthesizing the principal tools of nonlinear analysis: variational principles and fixed point analysis, and introduced the concept of a quasi-subdifferential operator which is a new class of abstract nonlinear operators.
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