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Generation, convergence and approximation of Lipschitz evolution operators in Banach spaces

Research Project

Project/Area Number 25400145
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Basic analysis
Research InstitutionChuo University

Principal Investigator

Yoshikazu Kobayashi  中央大学, 理工学部, 教授 (80092691)

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)
Project Period (FY) 2013-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
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)
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
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.

Report

(4 results)
  • 2015 Annual Research Report   Final Research Report ( PDF )
  • 2014 Research-status Report
  • 2013 Research-status Report
  • Research Products

    (21 results)

All 2016 2015 2014 2013

All Journal Article (8 results) (of which Peer Reviewed: 6 results,  Open Access: 3 results,  Acknowledgement Compliant: 2 results) Presentation (13 results) (of which Int'l Joint Research: 1 results,  Invited: 1 results)

  • [Journal Article] Abstract Cauchy problem for weakly continuous operators2016

    • Author(s)
      Toshitaka Matsumoto and Naoki Tanaka
    • Journal Title

      J. Math. Anal. Appl.

      Volume: 435 Issue: 1 Pages: 267-285

    • DOI

      10.1016/j.jmaa.2015.10.027

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] A stochastic coservation law nonhomogeneous Dirichlet boundary conditions,2016

    • Author(s)
      Kazuo Kobayasi and Dai Noboriguchi
    • Journal Title

      Act. Mathematica Vietnamica

      Volume: 未定

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Nonautonomous differential equations and Lipschitz evolution operators in Banach spaces2015

    • Author(s)
      Yoshikazu Kobayash, Naoki Tanaka and Yukino Tomizawa
    • Journal Title

      Hiroshima Mathematical Journal

      Volume: 45 Pages: 267-307

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Periodic points of some discontinuous maps2015

    • Author(s)
      Satomi Murakami and Hiroki Ohwa
    • Journal Title

      Nihonkai Mathematical Journal

      Volume: 26 Pages: 91-101

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Periodic points of some discontinuous mappings2015

    • Author(s)
      Satomi Murakami and Hiroki Ohwa
    • Journal Title

      The American Mathematical Monthly

      Volume: 122 Issue: 6 Pages: 581-587

    • DOI

      10.4169/amer.math.monthly.122.6.581

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Renomalized solutions to stochastic conservation laws2014

    • Author(s)
      Kazuo Kobayasi and Dai Noboriguchi
    • Journal Title

      早稲田大学教育・総合科学学術院 学術研究(自然科学編)

      Volume: 63 Pages: 31-45

    • Related Report
      2014 Research-status Report
  • [Journal Article] Nonlinear perturbations of a class of holomorphic semigroups of growth order α by comparison theorems for Volterra equations2013

    • Author(s)
      Toshitaka Matsumoto, Naoki Tanaka
    • Journal Title

      Nonlinear Anal

      Volume: 84 Pages: 146-175

    • DOI

      10.1016/j.na.2013.02.016

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Methods for proving some properties of the Ito integral in unfinite dimensions2013

    • Author(s)
      Kazuo Kobayasi and Dai Noboriguchi
    • Journal Title

      早稲田大学教育学部「学術研究」-自然科学編ー

      Volume: 62 Pages: 33-51

    • Related Report
      2013 Research-status Report
  • [Presentation] 確率外力を持つ退化放物型方程式の解の存在定理2016

    • Author(s)
      登口大, 小林和夫
    • Organizer
      日本数学会2016年度年会
    • Place of Presentation
      筑波大学
    • Year and Date
      2016-03-16
    • Related Report
      2015 Annual Research Report
  • [Presentation] サイズ構造モデルへの準線形理論的接近法2016

    • Author(s)
      松本敏隆,田中直樹
    • Organizer
      日本数学会2016年度年会
    • Place of Presentation
      筑波大学
    • Year and Date
      2016-03-16
    • Related Report
      2015 Annual Research Report
  • [Presentation] Mutational equation に対する適切性定理について2015

    • Author(s)
      小林良和, 田中直樹
    • Organizer
      第41回発展方程式研究会
    • Place of Presentation
      日本女子大学目白キャンパス
    • Year and Date
      2015-12-25
    • Related Report
      2015 Annual Research Report
  • [Presentation] 粘性項消滅法から現れる非線形波動方程式のエントロピー条件と安定性条件2015

    • Author(s)
      若月拓未, 應和宏樹
    • Organizer
      第41回発展方程式研究会
    • Place of Presentation
      日本女子大学目白キャンパス
    • Year and Date
      2015-12-25
    • Related Report
      2015 Annual Research Report
  • [Presentation] 弱連続作用素に対する抽象的Cauchy問題2015

    • Author(s)
      松本敏隆,田中直樹
    • Organizer
      第13回浜松偏微分方程式研究集会
    • Place of Presentation
      静岡大学工学部
    • Year and Date
      2015-12-22
    • Related Report
      2015 Annual Research Report
  • [Presentation] 弱連続作用素に対する抽象的Cauchy問題について2015

    • Author(s)
      松本敏隆, 田中直樹
    • Organizer
      ポテンシャル論セミナー
    • Place of Presentation
      名城大学理工学部
    • Year and Date
      2015-12-18
    • Related Report
      2015 Annual Research Report
  • [Presentation] Abstract Cauchy problem for weakly continuous operators2015

    • Author(s)
      松本敏隆, 田中直樹
    • Organizer
      第616回『応用解析』研究会
    • Place of Presentation
      早稲田大学理工学部
    • Year and Date
      2015-12-05
    • Related Report
      2015 Annual Research Report
  • [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
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 弱連続作用素に対する抽象的 Cauchy問題について2014

    • Author(s)
      松本敏隆、田中直樹
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      広島大学
    • Year and Date
      2014-09-25 – 2014-09-28
    • Related Report
      2014 Research-status Report
  • [Presentation] 確率保存型方程式に対する非斉次Dirichlet 問題の解の存在定理2014

    • Author(s)
      登口大,小林和夫
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      広島大学
    • Year and Date
      2014-09-25 – 2014-09-28
    • Related Report
      2014 Research-status Report
  • [Presentation] 乗法的確率項を持つ保存型方程式に対する初期値・境界値問題の一意性2014

    • Author(s)
      登口大,小林和夫
    • Organizer
      日本数学会年会
    • Place of Presentation
      学習院大学(東京、、目白)
    • Related Report
      2013 Research-status Report
  • [Presentation] n×n双曲型保存則方程式系に対する波面追跡法について2014

    • Author(s)
      應和宏樹
    • Organizer
      日本数学会年会
    • Place of Presentation
      学習院大学(東京、目白)
    • Related Report
      2013 Research-status Report
  • [Presentation] バナッハ空間における非線形発展作用素と常微分方程式2013

    • Author(s)
      小林良和
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      愛媛大学(松本)
    • Related Report
      2013 Research-status Report
    • Invited

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Published: 2014-07-25   Modified: 2019-07-29  

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