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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)
天野 要  愛媛大学, 工学部, 教授 (80113512)
Project Period (FY) 1997 – 1998
Project Status Completed (Fiscal Year 1998)
Budget Amount *help
¥4,900,000 (Direct Cost: ¥4,900,000)
Fiscal Year 1998: ¥1,700,000 (Direct Cost: ¥1,700,000)
Fiscal Year 1997: ¥3,200,000 (Direct Cost: ¥3,200,000)
Keywordselliptic equation / Poisson's equation / charge simulation method / radially symmetric / reaction-diffusion / standing pilse / cross-diffusion / Ginzburg-Landau equation / ギンツブルグ・ランダウ方程式 / 準線形楕円型方程式
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.

Report

(3 results)
  • 1998 Annual Research Report   Final Research Report Summary
  • 1997 Annual Research Report
  • Research Products

    (30 results)

All Other

All Publications (30 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
    • Related Report
      1998 Final Research Report Summary
  • [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
    • Related Report
      1998 Final Research Report Summary
  • [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
    • Related Report
      1998 Final Research Report Summary
  • [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
    • Related Report
      1998 Final Research Report Summary
  • [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
    • Related Report
      1998 Final Research Report Summary
  • [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
    • Related Report
      1998 Final Research Report Summary
  • [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
    • Related Report
      1998 Final Research Report Summary
  • [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
    • Related Report
      1998 Final Research Report Summary
  • [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
    • Related Report
      1998 Final Research Report Summary
  • [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
    • Related Report
      1998 Final Research Report Summary
  • [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
    • Related Report
      1998 Final Research Report Summary
  • [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
    • Related Report
      1998 Final Research Report Summary
  • [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
    • Related Report
      1998 Final Research Report Summary
  • [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
    • Related Report
      1998 Final Research Report Summary
  • [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
    • Related Report
      1998 Final Research Report Summary
  • [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
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 森下 博, 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の改良" 情報処理学会論文誌. (掲載予定).

    • Related Report
      1998 Annual Research Report
  • [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)

    • Related Report
      1998 Annual Research Report
  • [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.

    • Related Report
      1998 Annual Research Report
  • [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)

    • Related Report
      1998 Annual Research Report
  • [Publications] T.Gedeon, H.Kokubu, K.Mischaikow, H.Oka and J.Reineck: "Conley index for fast-slow systems I : One-dimensional slow variable" Journal of Dynamics and Differential Equations. (to appear).

    • Related Report
      1998 Annual Research Report
  • [Publications] S.Takeuchi and Y.Yamada: "Asymptotic Properities of a reaction-diffusion equation with degenerate p-Laplacian" Nonlinear Analysis,Theory,Methods & Applications. (to appear).

    • Related Report
      1998 Annual Research Report
  • [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)

    • Related Report
      1998 Annual Research Report
  • [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)

    • Related Report
      1998 Annual Research Report
  • [Publications] Y.Kabeya, E.Yanagida and S.Yotsutani: "Number of zeros of solutions to singular initial value problems" Tohoku J.Math.(to appear).

    • Related Report
      1997 Annual Research Report
  • [Publications] 森下博, 小林尚弘, 高市英明, 天野要, 四ッ谷晶二: "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)

    • Related Report
      1997 Annual Research Report
  • [Publications] X-Y.Chen, S.Jimbo and Y.Morita: "Stabilization of vorticies in Ginzburg-Landau equation with a variable diffusion coefficient" SIAM Journal of Mathematical Analysis. to appear.

    • Related Report
      1997 Annual Research Report
  • [Publications] Y.Morita: "Stabilization of solutions to the Ginzburg-Landau Equation with Neumann condition" Nonlinear Analysis:Theory,Methods and Applications. 30. 3939-3946 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] H.Kokubu, K.Mischaikov, Y.Nishiura, T.Takaishi, H.Oka: "Connecting orbit structure of monotone solutions in the shadow system" Journal of Differential Equations. (to appear).

    • Related Report
      1997 Annual Research Report
  • [Publications] T.Gedeon, H.Kokubu, K.Mishaikow, J.Reineck, H.Oka: "Conley index for fast-slow systems I:One-dimensional slow variable" Journal of Dynamics and Differential Equations. (to appear).

    • Related Report
      1997 Annual Research Report

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Published: 1997-04-01   Modified: 2016-04-21  

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