1998 Fiscal Year Annual Research Report

産業に現れる非線形発展系の応用解析と数値解析

Research Project

Project/Area Number	09640294
Research Institution	Nihon University
Principal Investigator	中村正彰日本大学, 理工学部, 助教授 (00017419)
Co-Investigator(Kenkyū-buntansha)	花田孝郎千葉工業大学, 工学部, 助教授 (40017447) 島近義日本大学, 理工学部, 助教授 (70059674) 竹沢照日本大学, 理工学部, 教授 (50059622)
Keywords	Phase sepatation / attractor / spinodal decomposition / stability / EOM system
Research Abstract	産業に現れる非線形現象を記述する非線形放物型方程式系のうち、相分離を記述する江口-沖-松村の方程式系について主に研究を進めた。とくに、方程式系の数学的定式化,長時間後の振舞を特徴付けるアトラクターの存在,および空間1次元の場合の定常解の安定性に関する数値シミュレーションの3つ分野に関して研究協力者と共に研究し次のような成果を得た。 1. 問題与えられた(u_0,υ_0)∈L^2に対して,次の方程式を満たす(u,υ)∈L^2(O,T;V)を求めよ.d/(dt)(u,φ)+LH(Δu,Δφ)-L((∂f(u,υ))/(∂υ),Δφ)=0 ∀φ∈V_1, d/(dt)(u,ψ)+MK(∇u,∇ψ)+M((∂f(u,υ))/(∂υ),ψ)=0 ∀ψ∈V_2 (u(0),ψ(0))=(u_0,υ_0) この弱問題に対して次の定理を得た. 定理任意に与えられたT>0と(u_0,υ_0)∈L^2 with υ_0∈L_4(Ω)に対して,つぎの条件を満たす(u,υ)が存在する. υ∈Cω(\|Ο,Υ\|;L^2)∩L^∞(0,T;L^2∩L^4)∩L^2(Ο,Υ;V_2)∩L^6(Ο,T;L^6(Ω)),∀T>0. 2. 江口-沖-松村方程式系はアトラクターをもつことを示した。 3. 1次元問題の数値シミュレーションを行った。この問題は研究途中である。

Research Products

(7 results)

All Other

All Publications (7 results)

[Publications] Naoyuki Ishimura and Masa Aki Nakamura: "Characterization on the long time behavior of the 2D Navier-Stokes equations" Pittman Reseaech Note in Math. Series.Vol.388. 38-44 (1998)
[Publications] Hitoshi Imai, Naoyuki Ishimura and Masa Aki Nakamura,: "Convergence of attractors for the simplified magnetic Benard system," Gakuto International Series, Mathematical Sciences and Applications. vol.11. 126-135 (1998)
[Publications] Hitoshi Imai, Naoyuki Ishimura and Masa Aki Nakamura,: "On the finite determination of the solutions for the MHD equations" Gakuto International Series, Mathematical Sciences and Applications. vol.11. 136-144 (1998)
[Publications] Hitoshi Imai, Naoyuki Ishimura and Masa Aki Nakamura(invited): "Convergence of fractal dimension of attractors for the simplified magnetic Benard system," The proceedings of third China-Japan seminar on numerical mathematics,. 73-81 (1998)
[Publications] Takao Hanada, Masa Aki Nakamura and Chikayoshi Shima,: "Numerical analysis of Eguchi-Oki-Matsumura equations." the proceedings of the fourth Japan-China joint-seminer on numeri-cal mathematics. (1999)
[Publications] H.Imai, T.Takeuchi, Masa Aki Nakamura, N.Ishimura: "A direct aproach to an inverse problem." the proceedings of the fourth Japan-China joint-seminar on numerical mathematics. (1999)
[Publications] 花田孝郎他5名: "数値計算法" オーム社, 199 (1998)

1998 Fiscal Year Annual Research Report

産業に現れる非線形発展系の応用解析と数値解析

Principal Investigator

中村 正彰 日本大学, 理工学部, 助教授 (00017419)

Research Products

[Publications] Naoyuki Ishimura and Masa Aki Nakamura: "Characterization on the long time behavior of the 2D Navier-Stokes equations" Pittman Reseaech Note in Math. Series.Vol.388. 38-44 (1998)

[Publications] Hitoshi Imai, Naoyuki Ishimura and Masa Aki Nakamura,: "Convergence of attractors for the simplified magnetic Benard system," Gakuto International Series, Mathematical Sciences and Applications. vol.11. 126-135 (1998)

[Publications] Hitoshi Imai, Naoyuki Ishimura and Masa Aki Nakamura,: "On the finite determination of the solutions for the MHD equations" Gakuto International Series, Mathematical Sciences and Applications. vol.11. 136-144 (1998)

[Publications] Hitoshi Imai, Naoyuki Ishimura and Masa Aki Nakamura(invited): "Convergence of fractal dimension of attractors for the simplified magnetic Benard system," The proceedings of third China-Japan seminar on numerical mathematics,. 73-81 (1998)

[Publications] Takao Hanada, Masa Aki Nakamura and Chikayoshi Shima,: "Numerical analysis of Eguchi-Oki-Matsumura equations." the proceedings of the fourth Japan-China joint-seminer on numeri-cal mathematics. (1999)

[Publications] H.Imai, T.Takeuchi, Masa Aki Nakamura, N.Ishimura: "A direct aproach to an inverse problem." the proceedings of the fourth Japan-China joint-seminar on numerical mathematics. (1999)

[Publications] 花田孝郎 他5名: "数値計算法" オーム社, 199 (1998)

中村正彰日本大学, 理工学部, 助教授 (00017419)

[Publications] 花田孝郎他5名: "数値計算法" オーム社, 199 (1998)