| Project/Area Number |
17K05294
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Shizuoka University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
小林 良和 中央大学, 理工学部, 共同研究員 (80092691)
渡邉 紘 大分大学, 理工学部, 准教授 (30609912)
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| Project Period (FY) |
2017-04-01 – 2020-03-31
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| Project Status |
Completed (Fiscal Year 2019)
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| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2019: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2018: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2017: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | 発展作用素 / 安定性条件 / 強退化放物型 / 適切性 / 変異方程式 / 強退化放物型方程式 / 準線形方程式 / 制約条件 / 準線形偏微分方程式 / 解析学 |
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| Outline of Final Research Achievements |
Abstract Cauchy problems for quasilinear evolution equations in Banach spaces are considered. We study the case where the infinitesimal generator depends on time variable. Under the assumption that the infinitesimal generator is strongly measurable with respect to time, we obtain time local existence and uniqueness, and time global existence and uniqueness results of strong solutions in time. Unique existence results and asymptotic behavior for entropy solutions to strongly degenerate parabolic equations with variable coefficients, and for entropy solutions to strongly degenerate parabolic systems with non-local terms are obtained. Phase field models related to grain boundary motions are considered as well. Uniqueness, smoothing effects, dissipativity of energy and asymptotic behavior of solutions are investigated. Finally, we extend the results of solvability for mutational equations and the theory of envelopes of nonlinear semigroups.
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| Academic Significance and Societal Importance of the Research Achievements |
発展方程式の抽象理論は、具体的な偏微分方程式の適切性の研究にある程度統一的な手法を与える道具の一つであるため、幅広く応用可能な理論を構築することは重要である。強退化放物型並びに結晶粒界モデルの研究は、具体的ないくつかの問題に関連するものであり、数値シミュレーションの信頼性の観点からも数学的な解析は不可欠である。変異方程式は比較的新しい手法であり、今後の研究の進展によって今まで取り扱いが困難であった問題への応用が期待されている。
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