• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Functional analytic research of hyperbolic equations with memory

Research Project

Project/Area Number 20540154
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionIbaraki University

Principal Investigator

OKA Hirokazu  茨城大学, 工学部, 教授 (90257254)

Co-Investigator(Kenkyū-buntansha) HIRASAWA Go  茨城大学, 工学部, 教授 (10434002)
UEKI Seiichirou  茨城大学, 工学部, 准教授 (70512408)
HOSOKAWA Takuya  茨城大学, 工学部, 准教授 (90553579)
Co-Investigator(Renkei-kenkyūsha) TANAKA Naoki  静岡大学, 理学部, 教授 (00207119)
Project Period (FY) 2008 – 2011
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords準線形双曲型方程式 / リプシッツ作用素半群 / 半線形発展方程式 / q-変形正規作用素 / 解析関数空間 / 荷重合成作用素 / Bloch空間 / ベルグマン空間 / ベルグマン・オーリッツ空間 / 半閉作用素 / q-距離 / 有界正則関数空間 / 積分作用素 / ソボレフ空間 / 単位的半単純可換Banach環 / 積分型作用素 / Fock型関数空間 / チェザロ型積分作用素 / Hardy空間 / Bergman型空間 / 軟解 / integral solution / Bergman空間 / Bargmann-Fock空間 / Cauchy-Euler型作用素 / Hyers-Ulam安定性
Research Abstract

A hyperbolic equation with memory and its related field are studied from the viewpoint of both sides of theory consideration to deal with the equation generally and systematically and the functional space in which the equation works place. As a result, abstract theories are developed to get global classical solutions for qualinear/semilinear evolution equations, and the characterizations are obtained of weighted composition operators on analytic function spaces and on the Bloch space. We also provided with the characterization of the contraction which corresponds injectively to the q-deformed normal operator.

Report

(6 results)
  • 2011 Annual Research Report   Final Research Report ( PDF )
  • 2010 Annual Research Report   Self-evaluation Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (62 results)

All 2012 2011 2010 2009 2008 Other

All Journal Article (37 results) (of which Peer Reviewed: 37 results) Presentation (23 results) Remarks (2 results)

  • [Journal Article] A product formula for semigroups of Lipschitz operators associated with abstract quasilinear evolution equations2012

    • Author(s)
      田中直樹
    • Journal Title

      Math. Nachr

      Volume: 285 Pages: 507-527

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] A product formula for semigroups of Lipschitz operators associated with abstract quasilinear evolution equations2012

    • Author(s)
      Naoki Tanaka
    • Journal Title

      Mathematische Nachrichten

      Volume: 285 Issue: 4 Pages: 507-527

    • DOI

      10.1002/mana.201010084

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Order bounded weighted composition operators mapping into the Bergman space2012

    • Author(s)
      S.Ueki
    • Journal Title

      Complex Anal.Oper.Theory

      Volume: (印刷中) Issue: 3 Pages: 549-560

    • DOI

      10.1007/s11785-011-0137-2

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Compactness of composition operators acting on weighted Bergman-Orlicz space2012

    • Author(s)
      A.K.Sharma, S.Ueki
    • Journal Title

      Ann.Polon.Math.

      Volume: (印刷中)

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A viability theorem of stochastic semilinear evolution equations2011

    • Author(s)
      田中直樹
    • Journal Title

      Israel Journal of Mathematics

      Volume: 186 Pages: 1-43

    • Related Report
      2011 Annual Research Report 2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Differences of weighted composition operators acting from Bloch space to H^∞2011

    • Author(s)
      細川卓也, 大野修一
    • Journal Title

      Trans. Amer. Math. Soc.

      Volume: 363 Pages: 5321-5340

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Global solvability for abstract semilinear evolution equations2010

    • Author(s)
      岡裕和, 田中直樹
    • Journal Title

      Math. Nachr.

      Volume: 283 Pages: 1171-1193

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] The q-deformed normal operator and its corresponding contraction2010

    • Author(s)
      平澤剛
    • Journal Title

      Far East J . Math. Sci.

      Volume: 46 Pages: 101-106

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Global solvability for abstract semilinear evolution equations2010

    • Author(s)
      岡裕和、田中直樹
    • Journal Title

      Math.Nachr. 283巻

      Pages: 1171-1193

    • Related Report
      2010 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] The q-deformed normal operator and its corresponding contraction2010

    • Author(s)
      平澤剛
    • Journal Title

      Far East J.Math.Sci. 46巻

      Pages: 101-106

    • Related Report
      2010 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Global solvability for abstract semilinear evolution equations2010

    • Author(s)
      Hirokazu Oka
    • Journal Title

      Math.Nachr.

      Volume: 283 Pages: 1171-1193

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Additively spectral-radius preserving surjections between unital semisimple commutative Banach algebras2010

    • Author(s)
      Osamu Hatori
    • Journal Title

      Cent.Eur.J.Math.

      Volume: 8 Pages: 597-601

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The q-deformed normal operator and its corresponding contraction2010

    • Author(s)
      Go Hirasawa
    • Journal Title

      Far East J.Math.Sci.

      Volume: 46 Pages: 101-106

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Algebraic properties of the distance between Sobolev spaces2010

    • Author(s)
      Go Hirasawa
    • Journal Title

      Int.J.Funct.Anal.Oper.Theory Appl.

      Volume: 2 Pages: 181-189

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Weighted composition operators on some function spaces of entire functions2010

    • Author(s)
      Seiichirou Ueki
    • Journal Title

      Bull.Belg.Math.Soc.Simon Stevin

      Volume: 17 Pages: 343-353

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On an integral-type operator acting between Bloch-type spaces on the unit ball2010

    • Author(s)
      Stevo Stevic
    • Journal Title

      Abstr.Appl.Anal.

      Volume: 2010

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A Lipschitz semigroup approach to two-dimensional Navier-Stokes equations2010

    • Author(s)
      Yoshikazu Kobayashi
    • Journal Title

      Nonlinear Anal.TMA 72

      Pages: 1820-1828

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Weighted composition operators and integral-type operators between weighted Hardy spaces on the unit ball2009

    • Author(s)
      Stevic Stevo, 植木誠一郎
    • Journal Title

      Discrete Dyn. Nat. Soc.

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Weighted composition operators and integral-type operators between weighted Hardy spaces on the unit ball2009

    • Author(s)
      Stevic Stevo、植木誠一郎
    • Journal Title

      Discrete Dyn.Nat.Soc.

    • Related Report
      2010 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Weighted composition operators and integral-type operators between weighted Hardy spaces on the unit ball2009

    • Author(s)
      S.Stevic
    • Journal Title

      Discrete Dyn.Nat.Soc.

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Integral-type operators acting between weighted-type spaces on the unit ball2009

    • Author(s)
      S.Stevic
    • Journal Title

      Appl.Math.Comput. 215

      Pages: 2464-2471

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Isometries of a Bergman-Privalov-type space on the unit ball2009

    • Author(s)
      S.Stevic
    • Journal Title

      Discrete Dyn.Nat.Soc.

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The essential norm of a weighted composition operator from the Bloch space to H^∞2009

    • Author(s)
      Takuya Hosokawa
    • Journal Title

      Bulletin of the Australian Mathematical Society 79

      Pages: 487-497

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Essential norms of weighted composition operators between weighted Bergman spaces of the ball2008

    • Author(s)
      植木誠一郎
    • Journal Title

      Acta Sci. Math.(Szeged)

      Volume: 7 Pages: 829-843

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Essential norms of weighted composition operators between weighted Bergman spaces of the ball2008

    • Author(s)
      植木誠一郎
    • Journal Title

      Acta Sci.Math.(Szeged) 74巻

      Pages: 829-843

    • Related Report
      2010 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Semigroups of locally Lipschitz operators associated with semilinear evolution equations of parabolic type2008

    • Author(s)
      Matsumoto,Toshitaka
    • Journal Title

      Nonlinear Analysis 69

      Pages: 4025-4054

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A Cauchy-Euler type factorization of operators2008

    • Author(s)
      Takahasi, Sin-Ei
    • Journal Title

      Tokyo Journal of Mathematics 31

      Pages: 489-493

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Compact weighted composition operators and multiplication operators between Hardy spaces2008

    • Author(s)
      Ueki, Sei-ichiro
    • Journal Title

      Abstract and Applied Analysis 2008

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Essential norms of weighted composition operators between weighted Bergman spaces of the ball2008

    • Author(s)
      Ueki, Sei-ichiro
    • Journal Title

      Acta Scientiarum Mathematicarum (Szeged) 74

      Pages: 829-843

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Weighted composition operators on the Bargmann-Fock space2008

    • Author(s)
      Ueki, Sei-ichiro
    • Journal Title

      International Journal of Modern Mathematics 3

      Pages: 231-243

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A perturbation of normal operators on a Hilbert space2008

    • Author(s)
      Miura, Takeshi
    • Journal Title

      Nonlinear Functional Analysis and Applications 13

      Pages: 291-297

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Order bounded weighted composition operators mapping into the Bergman space

    • Author(s)
      植木誠一郎
    • Journal Title

      Complex Anal. Oper. Theory

      Volume: (印刷中)

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Compactness of composition operators acting on weighted Bergman-Orlicz space

    • Author(s)
      A. K. Sharma, 植木誠一郎
    • Journal Title

      Ann. Polon. Math

      Volume: (印刷中)

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Differences of weighted composition operators acting form Bloch space to H∞

    • Author(s)
      細川卓也、大野修一
    • Journal Title

      Trans.Amer.Math.Soc. 掲載決定

    • Related Report
      2010 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Linear Combinations of Composition Operators on the Bloch spaces

    • Author(s)
      Takuya Hosokawa
    • Journal Title

      Canadian Mathematical Society (未定, 掲載決定)

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Eigenvalues of weighted composition operators on the Bloch space

    • Author(s)
      Takuya Hosokawa
    • Journal Title

      Integral Equation and Operator Theory (未定, 掲載決定)

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Differences of weighted composition operators acting from Bloch space to H^∞

    • Author(s)
      Takuya Hosokawa
    • Journal Title

      Transactions of the American Mathematical Society (未定, 掲載決定)

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Presentation] 増大度αの解析的半群の非線形摂動2012

    • Author(s)
      松本敏隆
    • Organizer
      日本数学会年会
    • Place of Presentation
      東京理科大学
    • Year and Date
      2012-03-28
    • Related Report
      2011 Final Research Report
  • [Presentation] 増大度αの解析的半群の非線形摂動2012

    • Author(s)
      松本敏隆
    • Organizer
      日本数学会年会
    • Place of Presentation
      東京理科大学(東京都)
    • Year and Date
      2012-03-28
    • Related Report
      2011 Annual Research Report
  • [Presentation] Integral type operators on H^∞2011

    • Author(s)
      細川卓也
    • Organizer
      関数環研究集会
    • Place of Presentation
      山形大学工学部
    • Year and Date
      2011-12-02
    • Related Report
      2011 Annual Research Report
  • [Presentation] 自己共役作用素の半径の計算方法について2011

    • Author(s)
      平澤剛
    • Organizer
      関数環研究集会
    • Place of Presentation
      山形大学工学部
    • Year and Date
      2011-12-01
    • Related Report
      2011 Annual Research Report
  • [Presentation] Linear isometries of some analytic function spaces which are contained in the Nevanlinna class2011

    • Author(s)
      S.Ueki
    • Organizer
      8th International ISAAC Congress
    • Place of Presentation
      Peoples' Friendship University of Russia, Moscow
    • Year and Date
      2011-08-24
    • Related Report
      2011 Annual Research Report
  • [Presentation] Iterations of weighted composition operators2011

    • Author(s)
      細川卓也
    • Organizer
      つくばセミナー
    • Place of Presentation
      筑波大学
    • Year and Date
      2011-03-08
    • Related Report
      2010 Annual Research Report
  • [Presentation] Iterations of weighted composition operators2011

    • Author(s)
      細川卓也
    • Organizer
      第19回宮代セミナー
    • Place of Presentation
      日本工業大学
    • Year and Date
      2011-01-08
    • Related Report
      2010 Annual Research Report
  • [Presentation] Differences of composition operators between H∞ and the Bloch space2010

    • Author(s)
      細川卓也
    • Organizer
      2010年度関数環研究集会
    • Place of Presentation
      信州大学
    • Year and Date
      2010-11-30
    • Related Report
      2010 Annual Research Report
  • [Presentation] ベルグマン・オーリッツ空間上の合成作用素2010

    • Author(s)
      植木誠一郎
    • Organizer
      2010年度関数環研究集会
    • Place of Presentation
      信州大学
    • Year and Date
      2010-11-29
    • Related Report
      2010 Annual Research Report
  • [Presentation] 半線形放物型方程式に付随するリプシッツ作用素半群に対する積公式2010

    • Author(s)
      松本敏隆
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      名古屋大学
    • Year and Date
      2010-09-25
    • Related Report
      2011 Final Research Report 2010 Annual Research Report 2010 Self-evaluation Report
  • [Presentation] Extreme points of the closed convex hull of composition operators on H^∞2010

    • Author(s)
      細川卓也
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      名古屋大学
    • Year and Date
      2010-09-25
    • Related Report
      2011 Final Research Report
  • [Presentation] Extreme points of the closed convex hull of composition operators H∞2010

    • Author(s)
      細川卓也
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      名古屋大学
    • Year and Date
      2010-09-25
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] Extreme points of the closed convex hull of composition operators on H∞2010

    • Author(s)
      細川卓也
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      名古屋大学
    • Year and Date
      2010-09-25
    • Related Report
      2010 Annual Research Report
  • [Presentation] Norms and essential norms of weighted composition operators between the Bloch space and H∞2010

    • Author(s)
      細川卓也
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      名古屋大学
    • Year and Date
      2010-09-25
    • Related Report
      2010 Annual Research Report
  • [Presentation] Weighted composition operators on some Fock-type spaces F_α^∞2009

    • Author(s)
      植木誠一郎
    • Organizer
      2009 Joint Meeting of KMS and AMS Special Sessions 20(Operator Theory in Analytic Function Spaces)
    • Place of Presentation
      Ewha Womans University
    • Year and Date
      2009-12-17
    • Related Report
      2009 Annual Research Report
  • [Presentation] 対称作用素と自己共役作用素の位相的関係について2009

    • Author(s)
      平澤剛
    • Organizer
      関数環研究集会
    • Place of Presentation
      日本大学薬学部
    • Year and Date
      2009-11-26
    • Related Report
      2011 Final Research Report 2010 Self-evaluation Report 2009 Annual Research Report
  • [Presentation] 1変数ベルグマン空間上のコンパクト荷重合成作用素について2009

    • Author(s)
      植木誠一郎
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      大阪大学
    • Year and Date
      2009-09-27
    • Related Report
      2011 Final Research Report 2010 Self-evaluation Report
  • [Presentation] 1変数ベルグマン空間上のコンパクト荷重合成作用素について2009

    • Author(s)
      植木誠一郎
    • Organizer
      日本数学会2009年度秋季総合分科会函数論分科会
    • Place of Presentation
      大阪大学
    • Year and Date
      2009-09-27
    • Related Report
      2009 Annual Research Report
  • [Presentation] Sobolev空間どうしの距離の代数的な性質について2009

    • Author(s)
      平澤剛
    • Organizer
      米沢数学セミナー
    • Place of Presentation
      山形大学工学部
    • Year and Date
      2009-07-07
    • Related Report
      2009 Annual Research Report
  • [Presentation] ベルグマン空間の間に作用する荷重合成作用素2008

    • Author(s)
      植木,誠一郎
    • Organizer
      函数論シンポジウム
    • Place of Presentation
      高知大学
    • Year and Date
      2008-10-12
    • Related Report
      2011 Final Research Report 2010 Self-evaluation Report
  • [Presentation] ベルグマン空間の間に作用する荷重合成作用素2008

    • Author(s)
      植木,誠一郎
    • Organizer
      第51回函数論シンポジウム
    • Place of Presentation
      高知大学
    • Year and Date
      2008-10-12
    • Related Report
      2008 Annual Research Report
  • [Presentation] ベルグマン空間上の荷重合成作用素に対する本質ノルム2008

    • Author(s)
      植木,誠一郎
    • Organizer
      日本数学会2008年度秋季総合分科会函数解析学分科会
    • Place of Presentation
      東京工業大学
    • Year and Date
      2008-09-25
    • Related Report
      2008 Annual Research Report
  • [Presentation] リプシッツ作用素半群入門-解が初期値にリプシッツ連続的に依存する微分方程式系への応用を目指して-2008

    • Author(s)
      田中,直樹
    • Organizer
      第30回発展方程式若手セミナー
    • Place of Presentation
      春日居びゅーほてる(山梨県笛吹市)
    • Year and Date
      2008-09-02
    • Related Report
      2008 Annual Research Report
  • [Remarks]

    • URL

      http://info.ibaraki.ac.jp/scripts/websearch/index.htm

    • Related Report
      2009 Annual Research Report
  • [Remarks]

    • URL

      http://info.ibaraki.ac.jp/scripts/websearch/index.htm

    • Related Report
      2008 Annual Research Report

URL: 

Published: 2008-04-01   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi