Generation, convergence and approximation of Lipschitz evolution operators in Banach spaces
| Project/Area Number |
25400145
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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 | Chuo University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
MATSUMOTO Toshitaka 静岡大学, 理学部, 教授 (20229561)
KOBAYASI Kazuo 早稲田大学, 教育・総合科学学術院, 教授 (80103612)
OHWA Hiroki 新潟大学, 自然科学系, 準教授 (10549158)
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| Project Period (FY) |
2013-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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| Keywords | 非線形発展方程式 / 非線形半群 / バナッハ空間 / 保存則系 / 非線形摂動 / 動力学的定式化 / リプシッツ作用素半群 / 弱連続生成素 / 区分的に線形な不連続関数 / ジャンプ / 運動力学的な解 / 乗法的確率外力項 / 保存則方程式系 / 弱連続作用素 / 抽象的Cauchy問題 / 非線形保存型方程式 / リプシッツ発展作用素 / 発展方程式 / 準縮小作用素 / リプシッツ作用素 / 準線形散逸的波動方程式 / 解析的半群 / 波面追跡法 / 保存型方程式 |
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| Outline of Final Research Achievements |
A new general class of Lipschitz evolution operators in Banach spaces is introduced and a characterization of the continuous infinitesimal generators of such evolution operators is obtained. It is given a necessary and sufficient condition for the existence of a weakly continuously differentiable solution to an abstract Cauchy problem in Banach spaces. Nonlinear perturbations of a holomorphic semigroup of fractional growth is studied through investigation of the associated Cauchy problems. Studying discontinuous mappings on intervals satisfying certain assumptions, it is shown that for such mappings there exist periodic points of period. In a kinetic formulation, it is obtained a result of uniqueness and existence of the initial-bounary value problem for a scalar first-order conservation law with a multicative noise.
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Report
(4 results)
Research Products
(21 results)
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[Presentation] Lipschitz Evolution Operators in Banach paces2015
Author(s)
Yoshikazu Kobayash, Naoki Tanaka, Yukino Tomizawa
Organizer
VII Symposium on Nonlinear Analysis
Place of Presentation
Faculty of Mathematics and Computer Science, Nicolaus Copernicus Universityersity
Year and Date
2015-09-14
Related Report
Int'l Joint Research
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