Mathematical analysis for nonlinear parabolic equations with degeneracy and mathematical models of grain boundary motion
| Project/Area Number |
25800086
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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
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| Research Institution | Oita University (2016)
SALESIAN POLYTECHNIC (2013-2015) |
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Principal Investigator |
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| Research Collaborator |
SHIRAKAWA Ken
Salvador Moll
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| Project Period (FY) |
2013-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | 退化放物型方程式 / 適切性 / エントロピー解 / 非局所量 / 結晶粒界現象 / 変分不等式 / エネルギー消散性 / 時間大域的挙動 / 退化放物型方程式系 / 変数係数 / 非線形解析 / 退化放物型 / 保存則 / 発展方程式 / 全変動汎関数 / 有界変動関数 |
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| Outline of Final Research Achievements |
First purpose of the research is to study about the construction of well-posedness theory for systems of strongly degenerate parabolic equations. In fact, we clarify well-posedness for single strongly degenerate parabolic equations with variable coefficients. Moreover, we show well-posedness for systems of it coupling by means of nonlocal quantities.
Second purpose of the research is to show the solvability for the mathematical models which are described by grain boundary motion under various situations. I fact, we show the solvability of the model with degenerate coefficients, solidification effect and heat exchanges. Moreover, we characterize the large time behavior of the solutions.
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Report
(5 results)
Research Products
(43 results)
