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On the stracture of solutions of partial differential eauqtions

Research Project

Project/Area Number 11640152
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

SAKURAI Tsutomu  Faculty of Science, SAITAMA UNIVERSITY, Associate Prpfessor, 理学部, 助教授 (40187084)

Co-Investigator(Kenkyū-buntansha) FUKUI Toshizumi  Faculty of Science, SAITAMA UNIVERSIY, Associate Professor, 理学部, 助教授 (90218892)
KOIKE Shigeaki  Faculty of Science, SAITAMA UNIVERSIY, Associate Professor, 理学部, 助教授 (90205295)
YANO Tamaki  Faculty of Science, SAITAMA UNIVERSIY, Profesor, 理学部, 教授 (10111410)
Project Period (FY) 1999 – 2000
Project Status Completed (Fiscal Year 2001)
Budget Amount *help
¥3,500,000 (Direct Cost: ¥3,500,000)
Fiscal Year 2000: ¥1,400,000 (Direct Cost: ¥1,400,000)
Fiscal Year 1999: ¥2,100,000 (Direct Cost: ¥2,100,000)
KeywordsMicrolocal analysis / Dispersion wave / Asymptotic expantion / Viscosity solution / Optimal control / Real singularities / Comparison theorem / 解析的準楕円性 / Symplectic characteristic / 擬微分作用素 / 特異点 / Bellman方程式
Research Abstract

The head investigator considered the asymptotic behavior of the surface waves of viscous incomplessible fluids. The suaface waves are governed by the Euler equation with the free boundary condition on the surface. We studied the dispersive behavior of the solutions to the linearlized equation. By using the Airy integral, we gave the asymptotic formula for the solutions at degenerate points. We also studied the coherent states of the light in the quantum mecanics. The coherent states are not mutually orthogonal but make a complete system of the quantum states of the light. Making use of the coherent states expantion, we obtained another derivation for the fundamental solutions to the Harmonic oscilators.
The head investigator writing a book on the partial differential equations. Some of the above results will be included in this book.

Report

(3 results)
  • 2001 Final Research Report Summary
  • 2000 Annual Research Report
  • 1999 Annual Research Report
  • Research Products

    (30 results)

All Other

All Publications (30 results)

  • [Publications] S.Koike, M.Bardi, P.Soravia: "On the pursuit-evasion game with state constrain"Discrete and Cotinnous Dynamical Systems. 6(2). 361-380 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] S.Koike, O.Alvarez, I.Nakayama: "Uniqlleness of lower semicontinuons viscosity solutions for the minimum time problem"SIAM Jounal on Control and Optimization. 38(2). 470-481 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] S.Koike, H.Ishii: "On ε-Optimal controls of state constraint problems"Annales de l'Institut Henri Poincare, Analyse Non Lineaire. 14(4). 473-502 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T.Fukui, L.Paunescu: "Modifled analytic trivialization for weighted homogeneons function-germs"Jounal of the Mathematical Society of Japan. 52. 433-446 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T.Fukui: "Congruence for real curves in toric surface and Newton polygons"Proceedings of XI Brazilian topology meeting(ed. S Firmo, D L Goncalves and O Saeki). 148-167 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T.Fukui, J.Weyman.: "Cohen-Macaulay properties of Thom-Boardman strata I : Morin's ideal"Proceedings of London Mathematical Society. 80(2). 257-303 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T.Fukui, L.Paunescu: "Stratification theory from the weighted point of view"Canadian Journal of Mathematics. 53. 73-97 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T.Fukui, T.-C.Kuo, L.Paunescu: "Constructing blow-analytic isomorphisms"Annales de l'Institut Fourier, Grenoble. 51. 1071-1087 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] S. Koike, M. Bardi, P. Soravia: "0n the pursuit-evasion game with state constrain"Discrete and Cotinuous Dynamical Systems. 6(2). 361-380 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] S. Koike, O. Alvarez, I. Nakayama: "Uniqueness of lower semicontinuous viscosity solutions for the minimum time problem"SIAM Journal on Control and Optimization. 38(2). 470-481 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] S. Koike, H. Ishii: "On ε-optimal controls of state constraint problems"Annales de l'Institut Henri Poincare. 14(4). 473-502 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T. Fukui, L. Paunescu: "Modified analytic trivialization for weighted homogeneous function-germs"Journal of the Mathematical Society of Japan. 52. 433-446 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T. Fukui: "Congruence for real curves in toric surface and Newton polygons"Proceedings of XI Brazilian topology meeting. 148-167 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T. Fukui, J. Weyman: "Cohen-Macaulay properties of Thom-Boardman strata I : Morin's ideal"Proceedings of London Mathematical Society. 80(2). 257-303 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T. Fukui, L. Paunescu: "Stratification theory from the weighted point of view"Canadian Journal of Mathematics. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T. Fukui, T.-C. Kuo, L. Paunescu: "Constructing blow-analytic isomorphisms"Annales de 1'Institut Fourier, Grenoble. (to apear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] S.Koike,M.Bardi and P.Soravia : "On the pursuit-evasion game with state constrain"Discrete and Cotinuous Dynamical Systems. 6(2). 361-380 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] S.Koike,O.Alvarez and I.Nakayama: "Uniqueness of lower semicontinuous viscosity solutions for the minimum time problem"SIAM Journal on Control and Optimization. 38(2). 470-481 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] S.Koike and H.Ishii: "ON ε-optimal controls of state constraint problems"Annales de l Institut Henri Poincare, Analyse Non Lineaire. 14(4). 473-502 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] T.Fukui and L.Paunescu: "Modified analytic trivialization for weighted homogeneous function-germs"Journal of the Mathematical Society of Japan. 52. 433-446 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] T.Fukui : "Congruence for real curves in toric surface and Newton polygons"Proceedins of XI Brazilian topology meeting (ed.S Firmo,D L Goncalves and O Saeki). 148-167 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] T.Fukui and J.Weyman : "Cohen-Macaulay properties of Thom-Boardman strata I : Morin's ideal "Proceedings of London Mathematical Society. 80(2). 257-303 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] T.Fukui and L.Paunescu: "Stratification theory from the weighted point of view"Canadian Journal of Mathematics, . (to appear).

    • Related Report
      2000 Annual Research Report
  • [Publications] T.Fukui,T.-C.Kuo and L.Paunescu : "Constructing blow-analytic isomorphisms"Annales de l Institut Fourier, Grenoble,. (to appear).

    • Related Report
      2000 Annual Research Report
  • [Publications] Toshizumi Fukui: "Butterfies and umbilics of stable perturbations of analytic map-germs (C^5,0) → (C^4,0) in "Singularity theory (edited by Bill Bruce & David Mond)""London Mathematical Society Lecture Note Series, Cambridge University Press. 263. 369-378 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] T. Fukui and L. Paunescu: "Modified analytic trivialization for weighted homogeneous function-germs"Journal of the Mathematical Society of Japan. 52. 433-446 (2000)

    • Related Report
      1999 Annual Research Report
  • [Publications] Toshizumi Fukui: "Congruence for real curves in toric surface and Newton polygons"Proceedings of XI-th Brazilian meeting of topology, World Scientific. (to appear).

    • Related Report
      1999 Annual Research Report
  • [Publications] T. Fukui and J. Weyman: "Cohen-Macaulay properties of Thom-Boardman strata I: Morin's ideal"Proceedings of London Mathematical Society. (to appear).

    • Related Report
      1999 Annual Research Report
  • [Publications] T. Fukui: "Newton polygon and topology of zero loci of real polynomials"Journal of the London Mathematical Society. (to appear).

    • Related Report
      1999 Annual Research Report
  • [Publications] S. Koike: "On the Bellman equations with varying control"Compositio Mathematica. (to appear).

    • Related Report
      1999 Annual Research Report

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Published: 1999-04-01   Modified: 2016-04-21  

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