2000 Fiscal Year Annual Research Report

数理科学に現れる偏微分方程式の解析的研究

Research Project

Project/Area Number	11440055
Research Institution	Osaka University
Principal Investigator	鈴木貴大阪大学, 大学院・理学研究科, 教授 (40114516)
Co-Investigator(Kenkyū-buntansha)	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)
Keywords	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
Research Abstract	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

Research Products

(19 results)

All Other

All Publications (19 results)

[Publications] T.Senba and T.Suzuki: "Weak solutions to a parabolic system of chemotaxis"J.Func.Anal..
[Publications] G.Haruda,T.Nagai,T.Senba,and T.Suzuki: "Concentration lemma, Brezis-Merle type inequality, and a parabolic system of chemotaxis."Adv.Differential Equations.
[Publications] T.Nagui,T.Senba,and T.Suzuki: "Chemabuitic collapse in a parabolic system of mathematical biology "Hiroshima Math.J.. 30. 463-497 (2001)
[Publications] T.Senba and T.Suzuki: "cpomotaitic collapse in a parabolic-elliptic system of mathmatical biology"Adr.Differential Equrtions. 6. 21-50 (2001)
[Publications] 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)
[Publications] 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)
[Publications] T.Suzuki: "A note on the stability of stationary solutions to a system of chemetacis"Comm.Contemporary Math.. 2. 373-383 (2000)
[Publications] Y.Naito and T.Suzuki: "Radial symmetry of sell-similar solutions for semilinear heat equations"J.Differential Equations. 163. 407-428 (2000)
[Publications] 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)
[Publications] A.Kokda and T.Suzuki: "Blow up Criteria for semilnear parabolic equations"J.Math.Anal.Appl.. 243. 127-139 (2000)
[Publications] 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)
[Publications] Y.Naito and T.Suzuki: "A note on the moving sphere method"Pacific J.Math.. 189. 107-116 (1999)
[Publications] 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)
[Publications] F.Colombini and T.,Nishituni: "On second order weakly hyperbolic equations and the Gevrey classes"Rend. Istit. Mat. Univ. Trieste. 31. 31-50 (2000)
[Publications] T.Wada: "Scattering theory for time-dependent Hartree-Fock type equation "Osaka J. Math.. 36. 905-918 (1999)
[Publications] T.Wada: "A remark on long range scattering for the Hartree type equation "Kyashu J. Math.. 54. 171-179 (2000)
[Publications] T.Wada: "Asymptotic expansion of the solution to the nonlinear Schrodinger equation with nonlocal interaction"J.Func.Anal..
[Publications] N.Kita and T.Wada: "Sharp asymptotic behavior of solutions to nonlinear Schrodinger equation in one spase dimension "Funkcial,Ekvac..
[Publications] 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 Fiscal Year Annual Research Report

数理科学に現れる偏微分方程式の解析的研究

Principal Investigator

鈴木 貴 大阪大学, 大学院・理学研究科, 教授 (40114516)

Research Products

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

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

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

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

[Publications] 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)

[Publications] 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)

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

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

[Publications] 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)

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

[Publications] 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)

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

[Publications] 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)

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

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

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

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

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

[Publications] 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)

鈴木貴大阪大学, 大学院・理学研究科, 教授 (40114516)