2000 年度実績報告書

数理科学に現れる偏微分方程式の解析的研究

研究課題

研究課題/領域番号	11440055
研究機関	大阪大学
研究代表者	鈴木貴大阪大学, 大学院・理学研究科, 教授 (40114516)
研究分担者	厚地淳大阪大学, 大学院・理学研究科, 講師 (00221044) 西谷達雄大阪大学, 大学院・理学研究科, 教授 (80127117) 小谷眞一大阪大学, 大学院・理学研究科, 教授 (10025463) 小田中紳二大阪大学, サイパーメディアセンター, 教授 (20324858) 和田健志大阪大学, 大学院・理学研究科, 助手 (70294139)
キーワード	走化性方程式 / 自由エネルギー / 爆発 / 量子化 / 局所化 / collapse / Langevin方程式 / Fokker-Planck方程式
研究概要	走化性方程式の解析的理論において大きな進展があった. 自己相互作用粒子系において摩擦と揺動の頂を導入した確率微分方程式であるLangevin方程式から出発し、統計力学的処理によってFokker-Planck方程式・走化性方程式(放物-楕円系)・指数型半線形楕円型境界値問題・勾配流方程式の関連が明らかにされ、全体を通して自由エネルギーに支配された爆発の量子化の現象であることがわかってきた.特に走化性方程式においてcollapseが量子化されることが解析的に証明されたことは特筆すべきことである

研究成果

(19件)

すべてその他

すべて文献書誌 (19件)

[文献書誌] T.Senba and T.Suzuki: "Weak solutions to a parabolic system of chemotaxis"J.Func.Anal..
[文献書誌] G.Haruda,T.Nagai,T.Senba,and T.Suzuki: "Concentration lemma, Brezis-Merle type inequality, and a parabolic system of chemotaxis."Adv.Differential Equations.
[文献書誌] T.Nagui,T.Senba,and T.Suzuki: "Chemabuitic collapse in a parabolic system of mathematical biology "Hiroshima Math.J.. 30. 463-497 (2001)
[文献書誌] T.Senba and T.Suzuki: "cpomotaitic collapse in a parabolic-elliptic system of mathmatical biology"Adr.Differential Equrtions. 6. 21-50 (2001)
[文献書誌] T.Senba and T.Suzuki: "Local and norm bohavior of blowup solutions to a parabolic system of chemotaxis"J.Korean Math.Soc.. 37. 929-942 (2000)
[文献書誌] R.Ikehata and T.Suzuki: "Somilinear parabolic equations involving cutical Sobolevexponent : local and asymptotic behavior of solutions"Integral and Differential Equations. 13. 869-901 (2000)
[文献書誌] T.Suzuki: "A note on the stability of stationary solutions to a system of chemetacis"Comm.Contemporary Math.. 2. 373-383 (2000)
[文献書誌] Y.Naito and T.Suzuki: "Radial symmetry of sell-similar solutions for semilinear heat equations"J.Differential Equations. 163. 407-428 (2000)
[文献書誌] T.Senba and T.Suzuki: "Some sturctures of the solution set for a stationary system of chemotaxis"Adr.Math.Sci.Appl.. 10. 191-224 (2000)
[文献書誌] A.Kokda and T.Suzuki: "Blow up Criteria for semilnear parabolic equations"J.Math.Anal.Appl.. 243. 127-139 (2000)
[文献書誌] S.Sakaguchi and T.Suzuki: "On a class of L^1-illposed quasilinear parabolicequations"Advances on Differntial Equtations."Adr.Differential Equations. 4. 671-696 (1999)
[文献書誌] Y.Naito and T.Suzuki: "A note on the moving sphere method"Pacific J.Math.. 189. 107-116 (1999)
[文献書誌] T.Nishitani and M.Takayama: "Regularity of solutions to non-uniformly characteristic boundary value problems for symmetric systems."Comm.Partial Differential Equations. 25. 987-1018 (2000)
[文献書誌] F.Colombini and T.,Nishituni: "On second order weakly hyperbolic equations and the Gevrey classes"Rend. Istit. Mat. Univ. Trieste. 31. 31-50 (2000)
[文献書誌] T.Wada: "Scattering theory for time-dependent Hartree-Fock type equation "Osaka J. Math.. 36. 905-918 (1999)
[文献書誌] T.Wada: "A remark on long range scattering for the Hartree type equation "Kyashu J. Math.. 54. 171-179 (2000)
[文献書誌] T.Wada: "Asymptotic expansion of the solution to the nonlinear Schrodinger equation with nonlocal interaction"J.Func.Anal..
[文献書誌] N.Kita and T.Wada: "Sharp asymptotic behavior of solutions to nonlinear Schrodinger equation in one spase dimension "Funkcial,Ekvac..
[文献書誌] Y.Isozoki,and S.Kotani.: "Asymptotic estimates for the first Putting time of fluiluating additive functionals of Brownion motion"Loct. Notes in Math.. 1729. 374-387 (2000)

2000 年度 実績報告書

数理科学に現れる偏微分方程式の解析的研究

研究代表者

鈴木 貴 大阪大学, 大学院・理学研究科, 教授 (40114516)

研究成果

[文献書誌] T.Senba and T.Suzuki: "Weak solutions to a parabolic system of chemotaxis"J.Func.Anal..

[文献書誌] G.Haruda,T.Nagai,T.Senba,and T.Suzuki: "Concentration lemma, Brezis-Merle type inequality, and a parabolic system of chemotaxis."Adv.Differential Equations.

[文献書誌] T.Nagui,T.Senba,and T.Suzuki: "Chemabuitic collapse in a parabolic system of mathematical biology "Hiroshima Math.J.. 30. 463-497 (2001)

[文献書誌] T.Senba and T.Suzuki: "cpomotaitic collapse in a parabolic-elliptic system of mathmatical biology"Adr.Differential Equrtions. 6. 21-50 (2001)

[文献書誌] T.Senba and T.Suzuki: "Local and norm bohavior of blowup solutions to a parabolic system of chemotaxis"J.Korean Math.Soc.. 37. 929-942 (2000)

[文献書誌] R.Ikehata and T.Suzuki: "Somilinear parabolic equations involving cutical Sobolevexponent : local and asymptotic behavior of solutions"Integral and Differential Equations. 13. 869-901 (2000)

[文献書誌] T.Suzuki: "A note on the stability of stationary solutions to a system of chemetacis"Comm.Contemporary Math.. 2. 373-383 (2000)

[文献書誌] Y.Naito and T.Suzuki: "Radial symmetry of sell-similar solutions for semilinear heat equations"J.Differential Equations. 163. 407-428 (2000)

[文献書誌] T.Senba and T.Suzuki: "Some sturctures of the solution set for a stationary system of chemotaxis"Adr.Math.Sci.Appl.. 10. 191-224 (2000)

[文献書誌] A.Kokda and T.Suzuki: "Blow up Criteria for semilnear parabolic equations"J.Math.Anal.Appl.. 243. 127-139 (2000)

[文献書誌] S.Sakaguchi and T.Suzuki: "On a class of L^1-illposed quasilinear parabolicequations"Advances on Differntial Equtations."Adr.Differential Equations. 4. 671-696 (1999)

[文献書誌] Y.Naito and T.Suzuki: "A note on the moving sphere method"Pacific J.Math.. 189. 107-116 (1999)

[文献書誌] T.Nishitani and M.Takayama: "Regularity of solutions to non-uniformly characteristic boundary value problems for symmetric systems."Comm.Partial Differential Equations. 25. 987-1018 (2000)

[文献書誌] F.Colombini and T.,Nishituni: "On second order weakly hyperbolic equations and the Gevrey classes"Rend. Istit. Mat. Univ. Trieste. 31. 31-50 (2000)

[文献書誌] T.Wada: "Scattering theory for time-dependent Hartree-Fock type equation "Osaka J. Math.. 36. 905-918 (1999)

[文献書誌] T.Wada: "A remark on long range scattering for the Hartree type equation "Kyashu J. Math.. 54. 171-179 (2000)

[文献書誌] T.Wada: "Asymptotic expansion of the solution to the nonlinear Schrodinger equation with nonlocal interaction"J.Func.Anal..

[文献書誌] N.Kita and T.Wada: "Sharp asymptotic behavior of solutions to nonlinear Schrodinger equation in one spase dimension "Funkcial,Ekvac..

[文献書誌] Y.Isozoki,and S.Kotani.: "Asymptotic estimates for the first Putting time of fluiluating additive functionals of Brownion motion"Loct. Notes in Math.. 1729. 374-387 (2000)

2000 年度実績報告書

鈴木貴大阪大学, 大学院・理学研究科, 教授 (40114516)