Solvability of differential equations from the point of view of the continuous dependence of solutions on their initial data
| Project/Area Number |
22540183
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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 | Shizuoka University |
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Principal Investigator |
TANAKA Naoki 静岡大学, 理学部, 教授 (00207119)
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| Co-Investigator(Kenkyū-buntansha) |
SHIMIZU Senjo 静岡大学, 創造科学技術大学院, 教授 (50273165)
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| Co-Investigator(Renkei-kenkyūsha) |
TAMURA Hideo 岡山大学, 大学院・自然科学研究科, 教授 (30022734)
ASAKURA Fumioki 大阪電気通信大学, 金融経済学部, 教授 (20140238)
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| Project Period (FY) |
2010 – 2012
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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2011: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | リプシッツ作用素半群 / 半線形発展方程式 / 準線形発展方程式 / 距離に似た汎関数 / 正則半群 / 安定性条件 / 近似定理 / projection method / mild solution / 移流拡散方程式系 / maximal solution / ボルテラ方程式 / Product formula / Analytic semigroup / Fractional power / Fractional step method / Semiliear evolution equation of parabolic type / Semigroup of Lipschitz operators / semilinear equation / quasilinear equation / product formula / growth condition / metric-like functional / convex functional / Zakharov equation / discrete semigroup |
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| Research Abstract |
We introduce two notions of semigroups of Lipschitz operators associated with semilinear and quasilinear equations respectively and establish approximation theorems for such semigroups. The feature is to propose a new type of stability condition which admits “error term”. We also discuss the solvability of semilinear equations with the help of comparison theorems for Volterra equations.
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Report
(4 results)
Research Products
(21 results)
