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Scattering theory of partial differential equations and its applications

Research Project

Project/Area Number 06302010
Research Category

Grant-in-Aid for Co-operative Research (A)

Allocation TypeSingle-year Grants
Research Field 解析学
Research InstitutionOsaka University

Principal Investigator

IKAWA Mitsuru  Osaka University, Faculty of Sciences, Professor, 理学部, 教授 (80028191)

Co-Investigator(Kenkyū-buntansha) IWASAKI Nobuhisa  Kyoto University, Graduate School of Sciences, Professor, 理学研究科, 教授 (70027374)
AGEMI Rentaro  Hokkaido University, Faculty of Sciences, Professor, 理学部, 教授 (10000845)
MOCHIZUKI Kiyoshi  Tokyo Metro.Univ., Faculty of Sciences, Professor, 理学部, 教授 (80026773)
NAKAO Mitsuhiro  Kyushyu University, Graduate School of Math.Sci., Professor, 数理学研究科, 教授 (10037278)
ICHINOSE Takashi  Kanazawa University, Faculty of Sciences, Professor, 理学部, 教授 (20024044)
西谷 達雄  大阪大学, 理学部, 教授 (80127117)
Project Period (FY) 1994 – 1995
Project Status Completed (Fiscal Year 1995)
Budget Amount *help
¥5,100,000 (Direct Cost: ¥5,100,000)
Fiscal Year 1995: ¥2,500,000 (Direct Cost: ¥2,500,000)
Fiscal Year 1994: ¥2,600,000 (Direct Cost: ¥2,600,000)
Keywordspartial differential equations / scattering theory / wave of earthquake / inverse problems / elastic equation / well posedness / nonlinear phenomenon / 散乱 / シュレ-ディンガー作用素 / 波動方程式 / 散乱核 / 極
Research Abstract

Using this grand-in-aid, we organized seberal conferences of small size and of middle size. We studied the theory of partial differential equation, theoretically and concret problems in our daily life. The investigators shared the fields of problems and all the participants co-operated in integrating the researchs by organized by investigators.
As we wrote in the above, we aimed to develope study of problems of partial differential equation in our daily life, and forcused the study to the inverse problems of partial differential equations, and developed the theoretial approach to these problems. Concerning the inverse problems, we experienced Kobe great earthquake during the period of our research. In fact, one of our main problem of research is a theoretical study of the inverse problem for the elastic wave, that is, the problem to determine the state of earth from the observation of the wave of earthquake. Even though Japan is a country of many earthquake, there are very few researcher in Mathematics. We have to develope the study of this inverse problems. Needless to say, we have to co-operate earth scientists, but we have to multiply the number of mathematicians interested in various problems related to earthquake.

Report

(3 results)
  • 1995 Annual Research Report   Final Research Report Summary
  • 1994 Annual Research Report
  • Research Products

    (22 results)

All Other

All Publications (22 results)

  • [Publications] T. Ichinose: "Some results on the relativistic Hamiltonian : Selfadjoint-ness and imaginary-time path integral" Differential Equations and Mathematical Physics. 116-130 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] A. Matsumura and M. Mei: "Nonlinear stability of viscous shock profile for a non-convex system of visco-elasticity" Comm. Math. Physics. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Y. Komatsu, T. Kano and A. Matsumura: "A bifurcation phenomenon for the Periodic solutions of Duffing equation," J. Math Kyoto Univ. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] K. Mochizuki and R. Suzuki: "Critical exponent and ciritical bouw-up for quasilinear parabolic equatoins" Israel J. Math.(to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] T. Nishitani: "On localization of a class of strongly hyperbolic systems" Osaka J. Math.32. 41-69 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] M. Nakao: "Decay of solutions of the wave equation with a local nonlinear dessipation" Math. Annalen. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] T.Ichinose: "Some results on the relativistic Hamiltonian : Selfadjointness and imaginary-time path integral" Diff. Equations and Math. Physics. 116-130 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] A.Matsumura and M.Mei: "Nonlinear stability of viscous shock profile for a non-convex system of visco-elasticity" Comm.Math.Physics. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Y.Komatsu, T.Kano and A.Matsumura: "A bifurcation phenomenon for the periodic solution of Duffing equation" J.Math.Kyoto Univ.(to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] K.Mochizuki and R.Suzuki: "Critical exponent and critical blow-up for quasilinear parabolic equation" Israel J.Math.(to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] T.Nishitani: "On localization of a class of strongly hyperbolic systems" Osaka J.Math.32. 41-69 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] M.Nakao: "Decay of solutions of the wave equation with a local nonlinear dessipation" Math.Annalen. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] T.Nishitani: "Symmetrization of hyperbolic systems with non-degenerate characteristics," J.Fun.Anal.132. 92-120 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] T.Nishitani: "On localization of a class of strongly hyperbolic systems" Osaka J.Math.32. 41-69 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] T.Ichinose: "Some results on the relativistic Hamiltonian:Selfadjointness and imaginary-time path integral" Diff.Equation Math.Physics. 116-130 (1955)

    • Related Report
      1995 Annual Research Report
  • [Publications] K.Mochizuki: "On energy decay and nodecay problems for wave equaion with nonlinear dissipatve term in R" J.Math.Soc.Japan. 47. 405-421 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] K.Mochizuki: "Critical exponent and ciritical bouw-up for quasilinear parabolic equatoins" to appear in Israel J.Math.

    • Related Report
      1995 Annual Research Report
  • [Publications] K.Mochizuki: "Energy decay and symptotic behavior ofsolutions to the wave equation with linear dissipation" to appear in Pual RIMS Kyoto Univ.

    • Related Report
      1995 Annual Research Report
  • [Publications] M.IKAWA: "On Zeta function and scattering poles for sever al couvex bodies" Journees “Equ.Derivees Parihelles",St.Jean de Mouts. II1-II14 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] M.Ikawa: "Poles of scattering matrix for two degenerate couvex bodies" Lecture notes in pure and applied math.,. 161. 33-62 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] T.Nishitani: "Symmetrijation of Hyperbolic systems with real coefficients" Ann.Scuo.Sup.Norm Pisa. 21. 98-130 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] K.Kajitani,T.Nishitani,S.Wakabayashi: "The Cauchy problem for hyperbolic operators of strong type" Duke Math.J.75. 353-408 (1994)

    • Related Report
      1994 Annual Research Report

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Published: 1994-04-01   Modified: 2016-04-21  

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