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1995 Fiscal Year Final Research Report Summary

Analysis and Computation of Nonlinear Structures

Research Project

Project/Area Number 05302013
Research Category

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

Allocation TypeSingle-year Grants
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionRyukoku University

Principal Investigator

IKEDA Tsutomu  Ryukoku Univ., Faculty of Science and Technology, Professor, 理工学部, 教授 (50151296)

Co-Investigator(Kenkyū-buntansha) MIYOSHI Tetsuhiko  Yamaguchi Univ., Faculty of Science, Professor, 理学部, 教授 (60040101)
FUJITA Hiroshi  Meiji Univ., School of Science and Technology, Professor, 理工学部, 教授 (80011427)
NISHIURA Masayasu  Hokkaido Univ., Research Institute for Electronic Sciences, Professor, 電子科学研究所, 教授 (00131277)
TABATA Masahisa  Hiroshima Univ., Faculty of Science, Professor, 理学部, 教授 (30093272)
OKAMOTO Hisashi  Kyoto Univ., Research Institute for Mathematical Sciences, Professor, 数理解析研究所, 教授 (40143359)
Project Period (FY) 1993 – 1995
KeywordsNonlinear Structures / Scientific Computing / Fluid Dynamics / Free Boundaries / Fracture Phenomena / Singular Points / Bifurcation Structure / Parallel Computation
Research Abstract

For the purpose of solving the structure of nonlinear phenomena and their dynamics, the present research project has been dealt with the following five major fields : (1) Nonlinear structure in fluid dynamics, (2) Dynamics of free boundaries, (3) Scientific computing of fracture phenomena, (4) Singular points appearing in differential equations, (5) Tracking of bifurcation structure.
Important results are as follows. Air flow computation around an automated guided vehicle (Tabata), Finite element analysis of axisymmetric flow problems (Tabata), Bifurcation of progressive waves of finite depth (Okamoto), Vortex sheet roll-up in the background shear flow (Okamoto) and Flow problems with unilateral boundary conditions (Fujita). Pattern selections for two breathers (Ikeda and Nishiura), Global bifurcation diagram of traveling pulses (Ikeda), Existence and stability of interfacial patterns in higher dimensional spaces (Nishiura), Singular limit systems derived from reaction-diffusion systems … More (Mimura), Numerical computation of generalized curve shortening equations (Tsutsumi) and Free boundaries in porous media (Kawarada) in (2). The arbitrary line method for elasto-plastic problems (Miyoshi) and Improved 4-node quadrilateral plate bending element (Kikuchi) in (3). Blow-up problems of degenerate parabolic equations (Tsutsumi and Matano) in (4). Reaction-diffusion systems and inertial manifolds (Morita) and Navier-Stokes flows down an inclined plate (Nishida) in (5). Other related topics have been also studied, Brain dynamics (Fujii) and Application of chaos theory to social sciences (Yamaguti) for instance.
The present project is characterized by the mathematical analysis in cooperation with numerical computation. The following results have been obtained in the field of the development of numerical methods : An improved conjugate gradient method for large systems of linear equations (Mitsui), Quadrature formulas for Fourier type integrals obtained by variable transformation (Mori), Computer aided proofs for bifurcation problems in equations of fluid dynamics (Nishida) and The domain dependence of convergence rate of a domain decomposition method (Fujita) for instance. Less

  • Research Products

    (44 results)

All Other

All Publications (44 results)

  • [Publications] T. Ikeda: "Numerical simulation for nonlinear oscillation of internal layers" Lecture Notes in Numerical and Applied Analysis. 14. 69-77 (1995)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T. Sakajo: "Numerical computation of vortex sheet roll-up in the background shearflow" to appear in Fluid Dynam. Res.17. (1995)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H. Fujita: "Distribution theoretic approach to fictitious domain method for Neumann problems" East-West J. Numer. Math.3. 111-126 (1995)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] F. Kikuchi: "An improved 4-node quadrilateral plate bending element of the Reissner-Mindlin type" to appear in Int. J. Eng. Anal. & Des.

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.Tabata: "Mixed and stabilized finite element approximations to axisymmetric flow problems" Computational Fluid Dynamics `94, John Wiley & Sons. 176-180 (1994)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T. Idogawa: "On numerical results for the linearizable generalized curve shortening equation" Nonlinear Times and Digest. 2. 173-178 (1995)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Y. Nishiura: "Some mathematical aspects of micro-phase separation in diblock copolymers" Physica D. 84. 31-39 (1995)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T. Nishida: "Bifurcation problems for equations of fluid dynamics and computer aided proof" Lecture Notes in Numerical and Applied Analysis. 14. 145-157 (1995)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H. Fujii: "A dynamical cell assembly model by mutual correlation-towards spatio-temporal coding by a system of coincidence detecting neurons" Proc. 1995 International Symposium on Nonlinear Theory and its Applications (NOLTA`95). 109-114 (1995)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H. Fujita: "Analytical and numerical approaches to stationary flow problems with leak and slip boundary conditions" Lecture Notes in Numerical and Applied Analysis. 14. 17-31 (1995)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T. Mitsui: "Symplectic numerical methods for dynamical systems and their applications" SEA Bull. Math.19. 37-49 (1995)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] X. -Y. Chen: "Finite-point extinction and continuity of interfaces in a nonlinear diffusion equation with strong absorption" J. Reine Angew. Math.459. 1-36 (1995)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] K. Kaminishi: "A method of arbitrary lines for elasto-plastic problems" Proc. Hellenic European Conf. on Mathematics and Informatics. 236-245 (1994)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] D. Furihata: "A finite difference scheme for the Cahn-Hilliard equation based on a Lyapunov functional" Gakuto International Series, Mathematical Sciences and Applications. 2. 347-385 (1993)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Y. Morita: "Nonlinear perturbation of boundary values for reaction-diffusion systems: inertial manifolds and their applications" SIAM Journal on Mathematical Analysis. 25. 1-37 (1994)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M. Yamaguti: "Discrete models in social sciences" Computers Math. Appl.28. 263-267 (1994)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 岡本 久: "非線型力学" 岩波書店, 165 (1995)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 菊地文雄: "有限要素法の数理-数学的基礎と誤差解析" 培風館, 278 (1994)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 田端正久: "微分方程式の数値解法II" 岩波書店, 122 (1994)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 根平邦人: ""左と右"で自然界を切る" 三共出版, 194 (1995)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 藤田 宏: "基礎解析I" 岩波書店, 102 (1994)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 藤田 宏: "最適化法" 岩波書店, 146 (1994)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 藤田 宏: "基礎解析II" 岩波書店, 255 (1995)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 藤田 宏: "関数解析" 岩波書店, 222 (1995)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 三井斌友: "微分方程式の数値解法I" 岩波書店, 116 (1993)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 森 正武: "複素関数論I" 岩波書店, 120 (1993)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 森 正武: "線形計算" 岩波書店, 121 (1994)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 森 正武: "複素関数論II" 岩波書店, 240 (1994)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T.Ikeda: "Numerical simulation for nonlinear oscillation of internal layrs" Lecture Notes in Numerical and Applied Analysis. 14. 69-77 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] T.Sakajo: "Numerical computation of vortex sheet roll-up in the background shear flow" to appear in Fluid Dynam.Res.17. (1995)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H.Fujita: "Distribution theoretic approach to fictitious domain method for Neumann problems" East-West J.Numer.Math.3. 111-126 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] F.Kikuchi: "An improved 4-node quadrilateral plate bending element of the Reissner-Mindlin type" to appear in Int.J.Eng.Anal.& Des.

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M.Tabata: "Mixed and stabilized finite element approximations to axisymmetric flow problems" Computational Fluid Dynamics '94, John Wiley & Sons. 176-180 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] T.Idogawa: "On numerical results for the linearizable generalized curve shortening equation" Nonlinear Times and Digest. 2. 173-178 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Y.Nishiura: "Some mathematical aspects of micro-phase separation in diblock copolymers" Physica D. 84. 31-39 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] T.Nishida: "Bifurcation problems for equations of fluid dynamics and computer aided proof" Lecture Notes in Numerical and Applied Analysis. 14. 145-157 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H.Fujii: "A dynamical cell assembly model by mutual correlation-towards spatio-temporal coding by a system of coincidence detecting neurons" Proc.1995 International Symposium on Nonlinear Theory and its Applications (NOLTA '95). 109-114 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H.Fujita: "Analytical and numerical approaches to stationary flow problems with leak and slip boundary conditions" Lecture Notes in Numerical and Applied Analysis. 14. 17-31 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] T.Mitsui: "Symplectic numerical methods for dynamical systems and their applications" SEA Bull.Math.19. 37-49 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] X.-Y.Chen: "Finite-point extinction and continuity of interfaces in a nonlinear diffusion equation with strong absorption1" J.Reine Angew.Math.459. 1-36 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K.Kaminishi: "A method of arbitrary lines for elasto-plastic problems" Proc.Hellenic European Conf.on Mathematics and Informatics. 236-245 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] D.Furihata: "A finite difference scheme for the Cahn-Hiliard equation based on a Lyapunov functional" Gakuto International Series, Mathematical Sciences and Applications. 2. 347-385 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Y.Morita: "Nonlinear perturbation of boundary values for reaction-diffusion systems : inertial manifolds and their applications" SIAM Journal on Mathematical Analysis. 25. 1-37 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M.Yamaguti: "Discrete models in social sciences" Computers Math.Appl.28. 263-267 (1994)

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

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Published: 1997-03-04  

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