1994 Fiscal Year Annual Research Report

非線形偏微分方程式系の総合的研究

Research Project

Project/Area Number	06640277
Research Institution	Waseda University
Principal Investigator	大谷光春早稲田大学, 理工学部, 教授 (30119656)
Co-Investigator(Kenkyū-buntansha)	小島清史早稲田大学, 理工学部, 教授 (30063689) 宮寺功早稲田大学, 教育学部, 教授 (50063293) 山田義雄早稲田大学, 理工学部, 教授 (20111825) 堤正義早稲田大学, 理工学部, 教授 (70063774) 郡敏昭早稲田大学, 理工学部, 教授 (50063730)
Keywords	非線形偏微分方程式 / 混合型方程式 / 非線形流体 / シュレディンガー方程式
Research Abstract	研究代表者及び理工学部所属の解析学分野分担者を中心とした、外部にも開かれた定期セミナーを早稲田大学理工学部内において週一回(計21回)開催した。この会(応用解析研究会)には、研究分担者のみならず、東京近郊の若手研究者が多く参加し、研究課題関連の話題について活発な討論、意見交換がおこなわれ、研究を遂行する上で非常に有意義であった。また研究経過発表会を数回おこなった。具体的成果については、個々の単独(非線形楕円形、放物型、双曲型、分散型)方程式に関する多くの成果のほかに、Davey-Stewartson(完全流体の表面波)方程式系に対し、弱解の存在と一意性及びその漸近挙動(時間とともに解のある種ノルムが零に近づく)が解明された。また、界面で化学反応を起こしている拡散方程式系、伝染病をモデル化した反応拡散系について、大域解の存在を示しその漸近挙動を決定した。更に、熱対流と非圧縮性粘性流との混合方程式系に対しては、流体の占める領域の境界が時間とともに変動する、非柱状領域における初期値境界値問題、周期問題の強解の存在と一意性が、柱状領域における熱伝導と粘性流に対してそれぞれ知られている結果を含む極めて一般的な枠組みで解決された。しかしながら、このように多くの成果があげられた一方、最終目標であったシュレディンガー混合型方程式系の多くを含む統一的理論を構築するという課題については、いくつかの有力な手がかりは得られたものの、達成するには至らなかった。今後の課題としたい。

Research Products

(18 results)

All Other

All Publications (18 results)

[Publications] Mitsuharu OTANI: "Nonlinear evolution equations with Time-dependent constraints" Aavances in Mathematical Sciences and Application. 3. 383-399 (1993/4)
[Publications] Mitsuharu OTANI: "Almost periochip soludions,of periodie systems governed by smpdnffenentiol operators" Preceeding of the American Math.Soeiety. (to appear). (1995)
[Publications] Hiroshi INOUE(and M.OTANI): "Heat convection equations in regrons with moving boundaries" Nonlenear Mathematical Probbemsin Industry II,Mathehatical Sciences and Applications Gakkotosho. 2. 571-581 (1993)
[Publications] Hiroshi INOUE(and M.OTANI): "Strong solution of initial boundary valve problems for bedat convection equations in noncyclindrical dowans" Nonlinear Analysis. (to appear). (1995)
[Publications] Tomoyuki IDOGAMA(and M.OTANI): "Analyticity and the bert possible constants for Sobolev-Polnaare ineaualties" Advences in Mathematical Scievces and Applications. 4. 71-78 (1994)
[Publications] Masayoshi TSUTSUMi: "Well-poredness of the Cancly proben for the long-wave-shat-wave systems" Jinlinear Analysis,T.M.A.23. 155-171 (1994)
[Publications] Masayoshi TSUTSUMI: "Decay of weak relations of the Davay-Stewartson systems" J.Month.Analy.Appl.182. 680-704 (1994)
[Publications] Masato IIDA(and Y.YAMADA): "Exponential convergence of solutions for a mathewatical model on chevnical interfacial reactions" Adrances in Mathematical Sciences and Applications. 3. 335-352 (1993/4)
[Publications] Hineki HOSHINO(and Y.YAMADA): "Asymptotic behavion of global solations for some reaction-diffusion systems" Nonlihear Analysis,TMA.23. 639-650 (1994)
[Publications] Kazanaga TANAKA: "A note on the existence of multiple homoclinic orbits for a pentarbed radial potential" Nonlinear Daff.Eq.and Appl.1. 149-162 (1994)
[Publications] Toshiaki KORI: "Index of the Dirac operator on S^4 and the infinite dimensional Grassmannian on S^3" Japanese Journal of Hath.(to appear).
[Publications] Toshiaki KORI: "Lie aigeira of the ahfimienael antomorpiasm on S^3 and its central extension" Kyoto Journal of math.(to appear).
[Publications] Toshiaki KORI: "4次元 Wess-Zamino-Wittenモデルの試み" 「非線形可積分系の数理」研究集会報告. (to appear).
[Publications] Junzo WADA: "Compact homomorplirm on alglbra of continuous fanctions" Tokyo Journal of Moth.(to appear).
[Publications] Naoki TANAKA and(Isao Miyadera): "C-Semi groups and the abstract Caucly problem II" Iutenational Conferece on Evolution Ebuations,Glasgow. (to appear). (1995)
[Publications] K.Makino(and Sia-icri SOZUKI): "Sofficiently decomposable sarfacer in 3-Splser" Yokohama Math.J.42. 95-102 (1994)
[Publications] Hirokazu OKA: "Integrated resolvent operators" Integral Equations and Applications. (to appear).
[Publications] Hirokazu OKA: "Second order livear volterra integrodifferential equations" Semigroup Forum. (to appeer).

1994 Fiscal Year Annual Research Report

非線形偏微分方程式系の総合的研究

Principal Investigator

大谷 光春 早稲田大学, 理工学部, 教授 (30119656)

Research Products

[Publications] Mitsuharu OTANI: "Nonlinear evolution equations with Time-dependent constraints" Aavances in Mathematical Sciences and Application. 3. 383-399 (1993/4)

[Publications] Mitsuharu OTANI: "Almost periochip soludions,of periodie systems governed by smpdnffenentiol operators" Preceeding of the American Math.Soeiety. (to appear). (1995)

[Publications] Hiroshi INOUE(and M.OTANI): "Heat convection equations in regrons with moving boundaries" Nonlenear Mathematical Probbemsin Industry II,Mathehatical Sciences and Applications Gakkotosho. 2. 571-581 (1993)

[Publications] Hiroshi INOUE(and M.OTANI): "Strong solution of initial boundary valve problems for bedat convection equations in noncyclindrical dowans" Nonlinear Analysis. (to appear). (1995)

[Publications] Tomoyuki IDOGAMA(and M.OTANI): "Analyticity and the bert possible constants for Sobolev-Polnaare ineaualties" Advences in Mathematical Scievces and Applications. 4. 71-78 (1994)

[Publications] Masayoshi TSUTSUMi: "Well-poredness of the Cancly proben for the long-wave-shat-wave systems" Jinlinear Analysis,T.M.A.23. 155-171 (1994)

[Publications] Masayoshi TSUTSUMI: "Decay of weak relations of the Davay-Stewartson systems" J.Month.Analy.Appl.182. 680-704 (1994)

[Publications] Masato IIDA(and Y.YAMADA): "Exponential convergence of solutions for a mathewatical model on chevnical interfacial reactions" Adrances in Mathematical Sciences and Applications. 3. 335-352 (1993/4)

[Publications] Hineki HOSHINO(and Y.YAMADA): "Asymptotic behavion of global solations for some reaction-diffusion systems" Nonlihear Analysis,TMA.23. 639-650 (1994)

[Publications] Kazanaga TANAKA: "A note on the existence of multiple homoclinic orbits for a pentarbed radial potential" Nonlinear Daff.Eq.and Appl.1. 149-162 (1994)

[Publications] Toshiaki KORI: "Index of the Dirac operator on S^4 and the infinite dimensional Grassmannian on S^3" Japanese Journal of Hath.(to appear).

[Publications] Toshiaki KORI: "Lie aigeira of the ahfimienael antomorpiasm on S^3 and its central extension" Kyoto Journal of math.(to appear).

[Publications] Toshiaki KORI: "4次元 Wess-Zamino-Wittenモデルの試み" 「非線形可積分系の数理」研究集会報告. (to appear).

[Publications] Junzo WADA: "Compact homomorplirm on alglbra of continuous fanctions" Tokyo Journal of Moth.(to appear).

[Publications] Naoki TANAKA and(Isao Miyadera): "C-Semi groups and the abstract Caucly problem II" Iutenational Conferece on Evolution Ebuations,Glasgow. (to appear). (1995)

[Publications] K.Makino(and Sia-icri SOZUKI): "Sofficiently decomposable sarfacer in 3-Splser" Yokohama Math.J.42. 95-102 (1994)

[Publications] Hirokazu OKA: "Integrated resolvent operators" Integral Equations and Applications. (to appear).

[Publications] Hirokazu OKA: "Second order livear volterra integrodifferential equations" Semigroup Forum. (to appeer).

大谷光春早稲田大学, 理工学部, 教授 (30119656)