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1998 Fiscal Year Final Research Report Summary

Resarchs on Solutions of Nonlinear Elliptic Equations and Numcrical Analysis

Research Project

Project/Area Number 09440087
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionRyukoku University

Principal Investigator

YOTSUTANI Shoji  Faculty of Science & Technology, Ryukoku Univ., Professor, 理工学部, 教授 (60128361)

Co-Investigator(Kenkyū-buntansha) YANAGIDA Eiji  Grad.School of Math.Sciences, Univ.of Tokyo, Assoc.Prof., 数理科学研究科, 助教授 (80174548)
YAMADA Yoshio  Faculty of Science & Technology, Waseda Univ., Professor, 理工学部, 教授 (20111825)
OKA Hiroe  Faculty of Science & Technology, Ryukoku Univ., Professor, 理工学部, 教授 (20215221)
MORITA Yoshihisa  Faculty of Science & Technology, Ryukoku Univ., Professor, 理工学部, 教授 (10192783)
IKEDA Tsutomu  Faculty of Science & Technology, Ryukoku Univ., Professor, 理工学部, 教授 (50151296)
Project Period (FY) 1997 – 1998
Keywordselliptic equation / Poisson's equation / charge simulation method / radially symmetric / reaction-diffusion / standing pilse / cross-diffusion / Ginzburg-Landau equation
Research Abstract

Head investigator S.Yotsutani proposed a very accurate numerical computation method to solve Poisson's equation by using a charge simulation method with H.Morishita, N.Kobayashi, H.Takaichi and K.Amano. Recently, He has succeeded to shorten the time of the calculation considerably and improve the accuracy with H.Morishita and K.Anjano, This method is in the conformity with the paerallel computing. Thus it is possible to know the detailed shape of solutions of nonlinear elliptic systems.
On the other hand, he developed the mathematical method of investigate the shape of radially symmetric solutions with Y.Kabeya and E.Yanagida. Recently, he has found the systematic change of variables to transform the differential equations arising from the elliptic equations to canonical form with E.Yanagida. Thus, relations between various equations studied one by one independently become very clear, and the understandings encourage the deep understanding of the propertites of each solution.
The reserach results of investigators are asfollows. T.lkeda invesitigate the instabiliz ation of the standing pulse solutions of bistable reaction-diffusion systems. Y.Morita showed stabilization of vorticies in the Ginzburg-Landau equation with a variable diffusion coefficient. H.Oka investigated the connecting orbit structure of monotone solutions in the shadow system. Y.Yamada proved the coexistence states for some population models with nonlinear cross-diffusion. E.Yanagida discoverd various new phenomena of the systems of parabolic equations and gave the proof of them.

  • Research Products

    (16 results)

All Other

All Publications (16 results)

  • [Publications] 森下 博, 小林尚弘, 高市英明 天野 要, 四ツ谷晶二: "代用電荷法によるポアソン方程式の数値計算" 情報処理学会論文誌. 38. 1483-1491 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Y.Kabeya, E.Yanagida and S.Yotsutani: "Number of zeros of solutions to singular initial value problems" Tohoku Math.J.50. 1-22 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H.Ikeda and T.Ikeda: "Bifurcation phenomena from standing pulse solutions of bistable reaction-diffusion systems" Journal of Dynamics and Differential Equations. to appcar.

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] X.Y.Chen, S.Jimbo and Y.Morita: "Stabilization of vorticies in the Ginzburg-Landau Equation with a variable diffusion coefficient" SIAM Journal of Mathematical Analysis. 29. 903-912 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H.Kokubu, K.Mischaikow, Y.Nishiura H.Oka and T.Takaishi: "Connecting orbit structure of monotone solutions in the shadow system" Journal of Differential Equations. 140. 309-364 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Y.Yamada: "Coexistence states for some population models with nonlinear cross-diffusion" Forma. 12. 153-166 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Y.Morita, E.Yanagida and S.Yotsutani (Eds.): "Proceedings of “Conference on Nonlinear Partial Differential Equations and Related Topics" Joint Research Center for Science and Technology of Ryukoku University, 98 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Y.Nishiura, I.Takagi and E.Yanagida (Eds.): "Proceedings of the International Conference on Asymptotics in Nonlinear Diffusive Systems" Tohoku Mathematical Publications, 8. Tohoku University, Mathematical Institute, Sendai, 262 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H.Morishita, N.Kobayashi, H.Takaichi, K.Amano, S.Yotsutani: "Numerical computation of Poisson's equation by the charge simulation method. (In Japanese.)" JohoshoriGakkai Ronbunshi. 38. 1483-1491 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Y.Kabeya, E.Yanagida and S.Yotsutani: "Number of zeros of solutions to singular inital value problems." Tohoku Math.J.50. 1-22 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H.Ikeda and T.Ikeda: "Bifurcation phenomena from standing pulse solutions of bistable reaction-diffusion systems." Journal of Dynamics and Differential Equations. (to appear.).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] X-Y.Chen, S.Jimbo and Y.Morita: "Stabilization of vorticies in the Ginzburg-Landau Equation with a variable diffusion coefficient." SIAM Journal of Mathematical Analysis. 29. 903-912 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H.Kokubo, K.Mischaikow, Y.Nishiura, H.Oka and T.Takaishi: "Connecting orbit structure of monotone solutions in the shadow system." Journal of Differential Equations. 140. 309-364 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Y.Yamada: "Coexistence states for some population models with nonlinearcross-diffusion." Forma. 12. 153-166 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Y.Morita, E.Yanagida and S.Yotsutani (Eds.): "Proceedings of "Conference on Nonlinear Partial Differential Equations." Joint Research Center for Science and Technology of Ryukoku University. 98 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Y.Nishiura, I.Takagi and E.Yanagida (Eds.): "Proceedings of the International Conference on Asymptoticsin Nonlinear Diffusive Systems." Tohoku Mathematical Publications, , 8, Tohoku University, Mathematical Institute, Sendai. 262 (1998)

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

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Published: 1999-12-08  

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