1997 Fiscal Year Annual Research Report

非線形初期値・境界値問題に対する領域分割・領域接合の研究

Research Project

Project/Area Number	09640297
Research Category	Grant-in-Aid for Scientific Research (C)
Research Institution	Meiji University
Principal Investigator	藤田宏明治大学, 理工学部, 教授 (80011427)
Co-Investigator(Kenkyū-buntansha)	河原田秀夫千葉大学, 工学部, 教授 (90010793) 桂田祐史明治大学, 理工学部, 講師 (80224484) 古橋朗蔵明治大学, 理工学部, 教授 (40061973) 今野礼二明治大学, 理工学部, 教授 (20061921) 森本浩子明治大学, 理工学部, 教授 (50061974)
Keywords	非線形 / 摩擦型境界条件 / 領域分割 / ポアッソン方程式 / ストークス方程式 / ナビエ・ストークス方程式 / 一般流束条件
Research Abstract	本研究の目指すところは数理科学・産業数学の諸分野における非線形偏微分方程式の応用解析的研究を特に非凡な境界条件・境界接合条件に焦点を合わせて遂行するものであるが,本年度において研究が進捗し成果をあげたものは次の通りである。 1.摩擦型の境界条件の研究(藤田・河原田);粘性非圧縮流に対する変分不等式を定式化に用いる当該境界値問題に対して,圧力をラグランジュ乗数関数として含む変分問題の基礎理論が整備された.また,その結果を用いて,鞍点型の変分的定式化および宇沢算法と呼ばれる型の反復法の研究が顕著な進歩を見せた.また,具体的な現象のモデルとして海岸に打ち寄せ砂浜に吸い込まれる海水の挙動の数理モデルが提出されたが,数値実験により納得できる結果が示された. 2.領域分割法の研究(藤田・桂田・斉藤他);領域の形状と収束の速さの関係を,藤田の方法を用いて解明する研究が,基本的なポアッソン方程式の場合については完成度の高い結果に到達した.ついで,ストークス方程式を対象とする研究に取り組んだが,Steklov-Poincare作用素の分数ベキの定義域の特徴付けなどの基礎的な考察がほぼ完了した. 3.一般流束条件のもとでのナビエ・ストークス方程式の可解性の研究(藤田・森本);しかるべき対象性のもとでの2次元流についての課題が藤田によりvirtual drainの方法により解決されたが,その発展として3次元の強い対象性のもとでの,しかし,興味ある結果が導かれた.また,一般流束条件を課せられた内壁をともなう2次元無限管内の流れの解析がほとんど完成された.

Research Products
(15 results)

All Other

All Publications (15 results)

[Publications] H. Fujita: "A remark on the existence of the Navier-Stokes flow with non-vanishing outflow condition" Gakuto Intern. Series, Math. Sci. Appl.10. 53-61 (1997)
[Publications] 藤田宏: "領域分割法の収束に関する解析的ならびに数値的研究,I," 明治大学技研紀要. 35-8. 103-135 (1997)
[Publications] H. Fujita: "Stability analysis of Navier-Stokes flow in annuli" Math. Meth. Appl. Sci.20. 959-978 (1997)
[Publications] H. Kawarada: "Navier-Stokes flows coupled with potential flow through porous media" DDM in Sciences and Engineering, John Wiley. 8. 403-410 (1997)
[Publications] H. Fujita: "An analytical study of optimal speed of convergence of iterations in DDM under certain shape assumptions of domains" Computational Sciences for 21st Century, John Wiley. 139-148 (1997)
[Publications] H. Fujita: "On stationary solutions to Navier-Stokes equation in symmetric plane domains under general outflow condition" Pitman, Research Notes in Mathematics Series,.
[Publications] H. Fujita: "On the rate of convergence of iterations in the domain-decomposition method" Proc. of 3rd Japan-China Joint Seminar on Numerical Mathematics.
[Publications] H. Fujita: "Variational inequalities for the Stokes equation with boundary conditions of friction type" Gakuto INtern. Series, Math. Sci. App.11.
[Publications] H. Kawarada: "Numerical method for a free surface flow on the basis of the fictious domain method" East-West J. of Numer. Math.5-1. 57-66 (1997)
[Publications] H. Kawarada: "Fuzzy optimazation method" Computational Science for 21st Sentury, Wiley. 643-651 (1997)
[Publications] H. Kawarada: "Multi-start fuzzy optimazation method" Gakuto Intern. Series, Math. Sci. Appl.11.
[Publications] H. Kawarada: "Wave motion breaking upon the shore" Gakuto Intern. Series, Math. Sci. Appl.11.
[Publications] H. Morimoto: "Stationary solutions for the Navier-Stokes equation and the Bousisnesq equations under general outflow condition" 数理解析研究所講究録. 1009.
[Publications] H. Morimoto: "Note on stationary Boussinesq equations in a bounded domain under general outflow condition" Proc. of NSEC6, 1997, Lithuania.
[Publications] H. Morimoto: "Perturbation of the Boussinesq flow in an annular domain with general outflow condition" Proc. Intern. Conf. on NS Equations, 1997, Italy.

1997 Fiscal Year Annual Research Report

非線形初期値・境界値問題に対する領域分割・領域接合の研究

Principal Investigator

藤田 宏 明治大学, 理工学部, 教授 (80011427)

Research Products

[Publications] H. Fujita: "A remark on the existence of the Navier-Stokes flow with non-vanishing outflow condition" Gakuto Intern. Series, Math. Sci. Appl.10. 53-61 (1997)

[Publications] 藤田宏: "領域分割法の収束に関する解析的ならびに数値的研究,I," 明治大学技研紀要. 35-8. 103-135 (1997)

[Publications] H. Fujita: "Stability analysis of Navier-Stokes flow in annuli" Math. Meth. Appl. Sci.20. 959-978 (1997)

[Publications] H. Kawarada: "Navier-Stokes flows coupled with potential flow through porous media" DDM in Sciences and Engineering, John Wiley. 8. 403-410 (1997)

[Publications] H. Fujita: "An analytical study of optimal speed of convergence of iterations in DDM under certain shape assumptions of domains" Computational Sciences for 21st Century, John Wiley. 139-148 (1997)

[Publications] H. Fujita: "On stationary solutions to Navier-Stokes equation in symmetric plane domains under general outflow condition" Pitman, Research Notes in Mathematics Series,.

[Publications] H. Fujita: "On the rate of convergence of iterations in the domain-decomposition method" Proc. of 3rd Japan-China Joint Seminar on Numerical Mathematics.

[Publications] H. Fujita: "Variational inequalities for the Stokes equation with boundary conditions of friction type" Gakuto INtern. Series, Math. Sci. App.11.

[Publications] H. Kawarada: "Numerical method for a free surface flow on the basis of the fictious domain method" East-West J. of Numer. Math.5-1. 57-66 (1997)

[Publications] H. Kawarada: "Fuzzy optimazation method" Computational Science for 21st Sentury, Wiley. 643-651 (1997)

[Publications] H. Kawarada: "Multi-start fuzzy optimazation method" Gakuto Intern. Series, Math. Sci. Appl.11.

[Publications] H. Kawarada: "Wave motion breaking upon the shore" Gakuto Intern. Series, Math. Sci. Appl.11.

[Publications] H. Morimoto: "Stationary solutions for the Navier-Stokes equation and the Bousisnesq equations under general outflow condition" 数理解析研究所講究録. 1009.

[Publications] H. Morimoto: "Note on stationary Boussinesq equations in a bounded domain under general outflow condition" Proc. of NSEC6, 1997, Lithuania.

[Publications] H. Morimoto: "Perturbation of the Boussinesq flow in an annular domain with general outflow condition" Proc. Intern. Conf. on NS Equations, 1997, Italy.

藤田宏明治大学, 理工学部, 教授 (80011427)