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2002 Fiscal Year Final Research Report Summary

Study on differential equations by asymptotic analysis

Research Project

Project/Area Number 13640191
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionSOPHIA UNIVERSITY

Principal Investigator

UCHIYAMA Koichi  Sophia Univ. Math. Professor, 理工学部, 教授 (20053689)

Co-Investigator(Kenkyū-buntansha) YOSHINO Kunio  Sophia Univ. Math. Lecturer, 理工学部, 講師 (60138378)
TAHARA Hidetoshi  Sophia Univ. Math. Professor, 理工学部, 教授 (60101028)
OUCHI Sunao  Sophia Univ. Math. Professor, 理工学部, 教授 (00087082)
HIRATA Hitoshi  Sophia Univ. Math. assistant, 理工学部, 助手 (20266076)
Project Period (FY) 2001 – 2002
Keywordsasymptotic analysis / differential equation / singularity / complex domain / integral representation / multi summability / Briot-Bouquet / Maillet
Research Abstract

A. Asymptotic analysis of differential equations in the complex domain.
S.Ouchi obtained integral representations of solutions with singularities of power type for a class containing Fuchsian linear PDEs and gave asymptotic behavior of solutions and Gevrey type estimates. He also proved multisummability of formal solutions to a class of linear PDEs he conjectured. H.Tahara, with H. Chen and Z.Luo, proved theorems of Maillet type for formal solutions to nonlinear PDEs with irregular singularity respect to space variables. He also obtained with J. Lope a sharp result on analytic continuation of solutions to a class of nonlinear PDEs of normal type. With H.Yamazawa, he determined the structure of solutions to a class of nonlinear PDEs of Fuchsian type without additional conditions on characteristic exponents.
B. Asymptotic analysis of differential equations in the real domain and related applied analysis.
K.Uchiyama, with L.Paredes, gave analytic expressions of solutions near their singularities for a nonlinear ODE, one dimensional p-elliptic Eq, using nonlinear ODE of Briot-Bouquet type in the complex domain. K.Yoshino characterized tempered distributions with support contained in convex proper cone, by asymptotic behavior of solutions to the heat equation, after T. Matsuzawa. H.Hirata gave relation between nonlinear parameter and the initial value space of semilinear Pintegro-DifiE interpolating the heat equation and the wave equation. He also constructed concrete solutions by Backlund transformations applied to trivial solutions to a certain 3rd order nonlinear PDE. S.Goto studied subfactors in operator algebra to compute principal graphs and to classify subfactors. M.Aoyagi studied numerical algorithms concerning triangle recognition, necessary for recognition of obstacles as complex after division of tetraheds after division of 3-dim obstacles.

  • Research Products

    (17 results)

All Other

All Publications (17 results)

  • [Publications] L.Paredes: "Analytic Singularities of Solutions to Certain Nonlinear Ordinary Differential Equations"Tokyo J. Math.. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] S.Ouchi: "Multisummability of formal solutions of some linear partial differential equations"J. Diff. Eqs. 185. 513-549 (2002)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H.Tahara: "On the singular solutions of nonlinear singular partial differential equations I"J. Math. Soc. Japan. 53. 711-729 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H.Chen: "Formal solutions of nonlinear first order totally characteristic type PDE with irregular ・・・"Ann. Inst. Fourier. 51. 1599-1620 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] J.E.C.Lope: "On the analytic continuation of solutions to nonlinear partial differential equations"J. Math. Pures Appl.. 81. 811-826 (2002)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H.Hirata: "Space-time estimates of linear flow and application to some nonlinear integro-differential ・・・"Adv. Diff. Eq.. 7. 217-236 (2002)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] L. Paredes, and K. Uchiyama: "Analytic Singularities of Solutions to Certain Nonlinear Ordinary Differential Equations associated with p-Laplacian"Tokyo J. Math. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] S. Ouchi: "Multisummability of formal solutions of some linear partial differential equations"J. Differential Equations. 185. 513-549 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] S. Ouchi: "The behaviors of singular solutions of partial differential equations in some class in the complex domain, Partial Differential Equations and Mathematical Physics, In Memory of Jean Leary, edited by K.Kajitani and J. Vaillant"Progress in Nonlinear Differential Equations and Their Applications, Birkhauser. vol 52. 177-194 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H. Tahara: "On the singular solutions of nonlinear singular partial differential equations I"J. Math. Soc. Japan. 53. 711-729 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H. Chen, Z. Luo and H. Tahara: "Some new results on the nonlinear singular partial differetial equations"Partial differential equations and spectral theory (edited by M.Demuth and B-W. Schultze), Birkhauser, Basel. 63-71 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H. Chen, Z. Luo, and H. Tahara: "Formal solutions of nonliear first order totally characteristic type PDE with irregular singularity"Ann. Inst. Fourier, Grenoble. 51. 1599-1620 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H. Tahara: "On the singularities of solutions of nonlinear partial differential equations in the complex domain"-Microlocal Analysis and Complex Fourier Analysis edited by T.Kawai and K.Fujita, World Sci.. 273-283 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] J.E.C. Lope, and H. Tahara: "On the analytic continuation of solutions to nonlinear partial differential equations"J. Math. Pures Appl.. 81. 811-826 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] T. Mandai, and H. Tahara: "Structure of solutions to Fuchsian systems of partial differential equations"Nagoya Math. J.. 169. 1-17 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H.Hirata, and C. Miao: "Space-time estimates of linear flow and application to some nonlinear integro-differential equations corresponding to fractional - order time derivative"Adv. Diff. Eq. 7. 217-236 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M.Aoyagi, and K.Tsuji: "Recognition of planar shapes by a semi-differential invariant for moving triangles"J. Comp. Appl. Math. Elsevier Science. (to appear).

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

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Published: 2004-04-14  

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