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2000 Fiscal Year Final Research Report Summary

Smoothing effect of Partial differential equations

Research Project

Project/Area Number 11440038
Research Category

Grant-in-Aid for Scientific Research (B).

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

Principal Investigator

KUNIKIKO Kajitani  Inst. Math., Professor, 数学系, 教授 (00026262)

Co-Investigator(Kenkyū-buntansha) NARIAKI Minami  Inst. Math., associate Prof., 数学系, 助教授 (10183964)
SEIICHIROU Wakabayashi  Inst. Math., Professor, 数学系, 教授 (10015894)
KAZUAKI Taira  Inst. Math., Professor, 数学系, 教授 (90016163)
HIROYUKI Takamura  Inst. Math., assistant Prof, 数学系, 講師 (40241781)
SINITI Doi  Inst. Math., associate Prof., 数学系, 助教授 (00243006)
Project Period (FY) 1999 – 2000
Keywordssmoothing effect / Schrodinger equation / dispersion equation / regularity / Gevrey class / Cauchy problem
Research Abstract

In the case of coefficients depending on time and places the problem of smoothing effect was considered to be very difficult technically. In this study we can find the new method to overcome this difficulty and are able to treat the more general dispersion equations. The results obtained in this study was published in the symposiums in Japan and in the international conference.
In particular it is a great progress to be able to prove the analytically smoothing effect of general dispersion equations.

  • Research Products

    (14 results)

All Other

All Publications (14 results)

  • [Publications] 梶谷邦彦: "Smoothing Effect in Gevreyclass for Schrodinger equations"Anr.Univ, Ferrara So,Math. XLV. 173-186 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 平良和昭: "A degenerate Neamann Problem for quass-linear elliptic integro-differential eguations"Math.Z.. 230. 679-694 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 高村博之: "The lifespan of classical solutions to systems of Nonlinear wave equation"Rend, Istit, Mat. Univ.Trieste. XXXI. 225-243 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 梶谷邦彦: "Propagation of analy.ticity of the solutions to the Cauchy problem"Ann.Scuola Norm, Sup.Pisa. 28. 471-487 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 土居伸一: "Smoothing effect for Schrodinger equations and global behavior of geodesic flow"Math.Ann. 318. 355-389 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 若林誠一郎: "Analytically smoothing effect for Schrodinger equation with variable eoefficients"Inst.Soc.Anal.Annl.Compnt.. 5. 185-219 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 若林誠一郎: "Classical Microlocal analysis in the space of Hyperfunction"Springer. 366 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] K.Kajitami: "Smoothing effect in Gevrey class for Schrodinger equations"Ann.Univ.Ferrara Sc.Math, XLV.. 173-186 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K.Taira: "A degenerate Neumann problem for quasi linear equations."Math.Z.. 230. 679-6 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H.Takamura: "The lift span of classical solution to systems of nonlinear wave equation"Rend.Inst.Math.Oniv Trieste XXXI. 225-243 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K.Kajitani: "Propagation of analyticity of the solution of systems"Ann.Scuola Norm.Sup Pisa. 28. 471-487 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] S.Poi: "Smoothing effect for Schrodinger equations and slabal be havior of seodesic flow"Math.Ann.. 318. 355-389 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] S.Wakabayashi: "Analytically smoothing effect for schrodinger equation with variable coefficients"Inst.Soc.Anal.Appl.Comput.. 5. 185-219 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] S.Wakabayashi: "Classical microlocal analysis in the Hyperfunction"Springer. 1-966 (2000)

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 2002-03-26  

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