1998 Fiscal Year Annual Research Report

偏微分方程式のための函数解析と実解析

Research Project

Project/Area Number	09440069
Research Institution	Tokyo University of Science
Principal Investigator	小松彦三郎東京理科大学, 理学部・第一部, 教授 (40011473)
Co-Investigator(Kenkyū-buntansha)	加藤圭一東京理科大学, 理学部・第一部, 講師 (50224499) 林仲夫東京理科大学, 理学部・第一部, 教授 (30173016) 宮地晶彦東京女子大学, 文理学部, 教授 (60107696) 宮島静雄東京理科大学, 理学部・第一部, 教授 (60130340) 岡沢登東京理科大学, 理学部・第一部, 教授 (80120179)
Keywords	佐藤超函数の畳み込み / 対称双曲系 / 非線形偏微方方程式 / 解の漸近挙動 / 解の解析性 / Triebel-Lizorkin空間 / Hordy型空間 / 作用素の評価
Research Abstract	小松は、1変数佐藤超函数の畳み込みに関する初等的理論を整備した。岡沢は、対称双曲系及びComplex Ginzburg-Landau方程式のCauchy問題に対して、それぞれ線形発展方程式論及び非線形半群論を適用し、新しい結果を得た。これらの方法は作用素について詳しい評価を必要としない利点がある一方、作用素の定義域が時間に依存しないことを確かめる必要がある。このための十分条件についても研究した。宮地は、R^nの領域上のTriebel-Lizorkin空間の元がすべてR^n上のTriebel-Lizorkin空間の元に拡張できるための条件を求め、いつ拡張作用素が存在するかを論じた。また、Calderon-Zygmund作用素や分数階積分作用素の積として定義される作用素のHardy型空間での評価を与えた。林は、非線形Schrodinger方程式、Hartree型方程式、Benjamin-Ono方程式、一般Korteweg-de Vries方程式などさまざまな発展型方程式に対して時刻が無限大になるときの解の漸近挙動について数多くの結果を得た。加藤は、昨年度に引き続き、非線形波動方程式、一般Korteweg-de Vries方程式などの解の解析性について研究した。

Research Products
(14 results)

All Other

All Publications (14 results)

[Publications] N.Okazawa: "Remarks on linear evolution equations of hyperbolic type in Hilbert opace" Adv.Math.Sci.Appl.8. 399-423 (1998)
[Publications] A.Unai and N.Okazawa: "Perturbations of nonlinear m-sectorial operaters and time-dependent Ginzburg-Landau equations" Dynamical Systems and Differential Equations(Springfield,1996). 259-266 (1998)
[Publications] V.Borisov and N.Okazawa: "Holomorphic families of linear operators in Banach spaces" SVT J Math.33. 189-205 (1997)
[Publications] A.Miyachi: "On the extension properties of Triebel-Lizorkin spaces" Hokkaido Math.J.27. 273-301 (1998)
[Publications] A,Miyachi: "Estimates for the product of singular integrals in Hardy type spaces" Proc.Conf.“Singular Integrals and Realted Topics".
[Publications] N.Hayashi and P.I.Naumkin: "Asymptotics in large time of solutions to nonbinear Schrodinger and Hartree equations" Amer.J.Math. 120. 369-389 (1998)
[Publications] N.Hayashi,P.I.Naumkin and T.Ozawa: "Scattering theory for the Hartree equation" SIAM J.Math.Anal.29. 1256-1267 (1998)
[Publications] N.Hayashi and P.I Naumkin: "Remarks on Scattering theory and large time asymptotics of solutions to Hartree type equations" SUT J.Math.34. 13-24 (1998)
[Publications] N.Hayashi and P.I.Naumkin: "Large time asymptotics of solutions to the generalized Korteweg-de Vries equation" J.Funct.Anal.159. 110-136 (1998)
[Publications] N.Hayashi,E.I.Kai-kina and P.I.Naumkin: "On the scattering theory for the cubic nonlinear Schrodinger and Hartree type equations in one space" Hokkaido Math.J.27. 651-667 (1998)
[Publications] N.Hayashi and P.I. Naumkin: "Large time asymptotics of solutions to the generalized Benjamin-One equation" Trans.Amer.Math.Soc.351. 109-130 (1999)
[Publications] N.Hayashi,E.I,Kaikina and P.I.Naumkin: "Large time behavior of solutions tothe generalized derivative nonlinear Schrodinger" Dis.Conti,Dyna.Sys,. 5. 93-106 (1999)
[Publications] 小松彦三郎: "ベクトル解析と多様体I・II" 岩波書店, 331 (1999)
[Publications] H.Komatsu: "An Introduction to the Theory of generalized Functions" Dept.of Math.,Science Univ of Tokyo, 180 (1999)

1998 Fiscal Year Annual Research Report

偏微分方程式のための函数解析と実解析

Principal Investigator

小松 彦三郎 東京理科大学, 理学部・第一部, 教授 (40011473)

Research Products

[Publications] N.Okazawa: "Remarks on linear evolution equations of hyperbolic type in Hilbert opace" Adv.Math.Sci.Appl.8. 399-423 (1998)

[Publications] A.Unai and N.Okazawa: "Perturbations of nonlinear m-sectorial operaters and time-dependent Ginzburg-Landau equations" Dynamical Systems and Differential Equations(Springfield,1996). 259-266 (1998)

[Publications] V.Borisov and N.Okazawa: "Holomorphic families of linear operators in Banach spaces" SVT J Math.33. 189-205 (1997)

[Publications] A.Miyachi: "On the extension properties of Triebel-Lizorkin spaces" Hokkaido Math.J.27. 273-301 (1998)

[Publications] A,Miyachi: "Estimates for the product of singular integrals in Hardy type spaces" Proc.Conf.“Singular Integrals and Realted Topics".

[Publications] N.Hayashi and P.I.Naumkin: "Asymptotics in large time of solutions to nonbinear Schrodinger and Hartree equations" Amer.J.Math. 120. 369-389 (1998)

[Publications] N.Hayashi,P.I.Naumkin and T.Ozawa: "Scattering theory for the Hartree equation" SIAM J.Math.Anal.29. 1256-1267 (1998)

[Publications] N.Hayashi and P.I Naumkin: "Remarks on Scattering theory and large time asymptotics of solutions to Hartree type equations" SUT J.Math.34. 13-24 (1998)

[Publications] N.Hayashi and P.I.Naumkin: "Large time asymptotics of solutions to the generalized Korteweg-de Vries equation" J.Funct.Anal.159. 110-136 (1998)

[Publications] N.Hayashi,E.I.Kai-kina and P.I.Naumkin: "On the scattering theory for the cubic nonlinear Schrodinger and Hartree type equations in one space" Hokkaido Math.J.27. 651-667 (1998)

[Publications] N.Hayashi and P.I. Naumkin: "Large time asymptotics of solutions to the generalized Benjamin-One equation" Trans.Amer.Math.Soc.351. 109-130 (1999)

[Publications] N.Hayashi,E.I,Kaikina and P.I.Naumkin: "Large time behavior of solutions tothe generalized derivative nonlinear Schrodinger" Dis.Conti,Dyna.Sys,. 5. 93-106 (1999)

[Publications] 小松彦三郎: "ベクトル解析と多様体I・II" 岩波書店, 331 (1999)

[Publications] H.Komatsu: "An Introduction to the Theory of generalized Functions" Dept.of Math.,Science Univ of Tokyo, 180 (1999)

小松彦三郎東京理科大学, 理学部・第一部, 教授 (40011473)