1999 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
研究種目	基盤研究(B)
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	西谷達雄大阪大学, 大学院・理学研究科, 教授 (80127117) 伊達悦朗大阪大学, 大学院・理学研究科, 教授 (00107062) 小谷眞一大阪大学, 大学院・理学研究科, 教授 (10025463) 磯崎洋大阪大学, 大学院・理学研究科, 助教授 (90111913) 松村昭孝大阪大学, 大学院・理学研究科, 教授 (60115938)
キーワード	走化性方程式 / 脳磁図分析 / 弾性波動 / 数理ファイナンス / 散乱理論 / 共形場理論 / 圧縮性粘性流体方程式 / 双曲型方程式系
研究概要	解析学の立場から様々な数理現象を研究し、未解決な現象の解明と新しい問題の定式化を行った。偏微分方程式からは、数理生物学において広く観察される走化性について、最近の実解析学の成果の適用により、時間大域解の挙動や爆発現象の解明等画期的な成果があった。また医学数学の最新の研究テーマである脳磁回分析では、新しい数学的定式化と崩芽的な研究が行われた。波動現象では、弾性体に関する回析によって生じた表面波の偏りについて基本的で深い結果が得られた。統計力学・確率解析からのアプローチでは、ランダムメディア・数理ファイナンスで求められる、拡散過程のいろいろな汎関数や期待値の漸近的性質を研究し、特に初期値がランダムな Burgers方程式において成果をあげた。この他には、Harbree 型ポテンシャルをもつ Schiodingers方程式、共形場理論と確定特異点型偏微分方程式、圧縮性粘性流体方程式、双曲型方程式系の適切性などを研究し、現象の解明を行った。

研究成果

(33件)

すべてその他

すべて文献書誌 (33件)

[文献書誌] T. SUZUKI: "A note on the stability of stationary solutions to a system of chemotaxis"Communications in Contemporary Mathematics. (to appear).
[文献書誌] T. NAGAI, T. SENBA,and T. SUZUKI: "Chemotactic collapse in a parabolic system of mathematical biology"Hiroshima Math J.. (to appear).
[文献書誌] T. SENBA and T. SUZUKI: "Chemotactic collapse in a parabolic-elliptic system of mathematical biology"Advances on Differential Equations. to appear).
[文献書誌] A. KOHDA and T. SUZUKI: "Blow-up criteria for semilinear parabolic equtations"J. Math. Anal. Appl.. to appear).
[文献書誌] T. SENBA and T. SUZUKI: "Local and norm behavior of blowup solutions to a parabolic system of Chemotaxis"J. Korean Math. Soc.. to appear).
[文献書誌] Y. NAITO and T. SUZUKI: "Radical symmetry of self-similar solutions for semilinear heat equation"J. Differntial Equations. to appear).
[文献書誌] T. SENBA and T. SUZUKI: "Some Structure of the solution set for a stationary system of chemotaxis"Adv. Math. Sci. Appl.. to appear).
[文献書誌] A. HAMATAKE and T. SUZUKI: "Singular solutions for a nonlinear Dirichlet problem"Communications in Applied Analysis. to appear).
[文献書誌] R. IKEHATA and T. SUZUKI: "Semilinear parabolic equations involving critical Soboler exponent : local and asymptotic behavior of solutions"Integral and Differntial Equations. to appear).
[文献書誌] S. SAKAGUCHI and T. SUZUKI: "On a class of L^1-illposed quasilinear parabolic equations"Advances on Differntial Equtations. 4. 671-696 (1999)
[文献書誌] Y. ADACHI, H. KADO,and T. SUZUKI: "Parameter descending method and the magnetoence phalography"Information. 2. 443-458 (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] Y. ISOZAKI and S. KOTANI: "Asymptotic estimates for the first hitting time of fluctuating addictive functionals on Browman motion"Seminar on Probability. (to appear).
[文献書誌] S. BENVENUTI and T. NISHTANI: "Necessary conditions for the hyperbolicity of 2×2 systems"Japanese J. Math.. 25. 377-408 (1999)
[文献書誌] F. COLOMBINI and T. SUZUKI: "Two by Two strongly hyperbolic systems and Gevreg classes"Ann. Mat. Univ. Ferrara. (to appear).
[文献書誌] A. MATSUMURA and M. MEI: "Convergence to travelling fronts of solutions of the p-system with viscosity in the presence of a boundary"Arch. Rational Mech. Anal.. 146. 1-22 (1999)
[文献書誌] A. MATSUMURA and K. NISHIHARA: "Global asymptotics toward rarefaction wave for solutions of the viscous p-system with boundary effect"Quart. Appl. Math.. (to appear).
[文献書誌] K. HIRACHI,G. KOMATSU and N. NAKAZAWA: "CR inovariants of weight five in the Bergman hernel"Adv. Math.. 143. 185-250 (1999)
[文献書誌] K. HIRACHI and G. KOMATSU: "Local Sobolev-Beryman kernels of stuctly pseudoconvex domains"Analysis acid Geometry on Several Complex Variables (Birk hauser). 63-96 (1999)
[文献書誌] 原澤隆一,四方順司,鈴木譲,今井秀樹: "楕円曲線暗号におけるMOV帰着とFR帰着の比較について"電子情報通信学会論文集A. 1278-1290 (1999)
[文献書誌] J. SUZUKI: "Learning Baysian belief networks based on the MDL principle : basic properties"IEI. CE Trans. on Foundamentals. 82A. (1999)
[文献書誌] J. SHIKATA,Y. ZHENG,J. SUZUKI,H. IMAI: "Realizing the Menezes-Okamoto-Vanstone (MOV) reduction efficiently for general alliptis curves"IEI. CE Trans. on Foundamentals. (to appear).
[文献書誌] A. MATSUO and K. NAGATOMO: "A note on free bosanic vertex algebra and its conformal vectors"J. Algebra. 212. 365-418 (1999)
[文献書誌] A. MATSO and K. NAGATOMO: "Axioms for vertex algebra and the locality of quantum fields"Memories of Math Soc. Japan. 4. (1999)
[文献書誌] M. MIKI.: "Toroidal and level O U^'_8 (<sl>^^^∧_<n+1>) actions on U_8(<gl>^^^∧_<n+1>) modules"J. Math. Phys.. 40. 3191-3210 (1999)
[文献書誌] A. Atsuji: "A Casorati -Weierstrass theorem for holomorphic maps invariant Q-field of helomorphic diffusions"Bull. Sci. Math.. 123. 371-383 (1999)
[文献書誌] A. Atsuji: "Remarks on harmoric maps into a core for stochastic complete manifolds"Proc. Japan Acad.. 75. 105-108 (1999)
[文献書誌] A. Atsuji: "A remark on a limiting behavior of the occupation times on unbounded domains of Browman motion"J. Math. Sci. University of Tokyo. (to appear).
[文献書誌] K. HIRACHI: "Construction of boundary onvariants and the logarithmic singularity of the Borgman kernel"Ann. Math.. (to appear).
[文献書誌] T. MORIOKA: "Regulari te de ondes Eastiques dans la reian Glancing des ondes P."Publ. RIMS. Kyoto Univ.. 35・4. 599-619 (1999)
[文献書誌] T. WADA: "A remark on long range scattering for the Hartree type eqation"Kyusyu J. Math.. (to appear).
[文献書誌] G. KOMATSU and M. KURANISHI(ed.): "Analysis and Geometry on Several Complex Variables Proceedings of 40 th Toniguchi Symposium"Birkkauser. (1999)
[文献書誌] 鈴木譲: "情報源符号化・無歪みデータ圧縮"培風館. (1999)

1999 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. SUZUKI: "A note on the stability of stationary solutions to a system of chemotaxis"Communications in Contemporary Mathematics. (to appear).

[文献書誌] T. NAGAI, T. SENBA,and T. SUZUKI: "Chemotactic collapse in a parabolic system of mathematical biology"Hiroshima Math J.. (to appear).

[文献書誌] T. SENBA and T. SUZUKI: "Chemotactic collapse in a parabolic-elliptic system of mathematical biology"Advances on Differential Equations. to appear).

[文献書誌] A. KOHDA and T. SUZUKI: "Blow-up criteria for semilinear parabolic equtations"J. Math. Anal. Appl.. to appear).

[文献書誌] T. SENBA and T. SUZUKI: "Local and norm behavior of blowup solutions to a parabolic system of Chemotaxis"J. Korean Math. Soc.. to appear).

[文献書誌] Y. NAITO and T. SUZUKI: "Radical symmetry of self-similar solutions for semilinear heat equation"J. Differntial Equations. to appear).

[文献書誌] T. SENBA and T. SUZUKI: "Some Structure of the solution set for a stationary system of chemotaxis"Adv. Math. Sci. Appl.. to appear).

[文献書誌] A. HAMATAKE and T. SUZUKI: "Singular solutions for a nonlinear Dirichlet problem"Communications in Applied Analysis. to appear).

[文献書誌] R. IKEHATA and T. SUZUKI: "Semilinear parabolic equations involving critical Soboler exponent : local and asymptotic behavior of solutions"Integral and Differntial Equations. to appear).

[文献書誌] S. SAKAGUCHI and T. SUZUKI: "On a class of L^1-illposed quasilinear parabolic equations"Advances on Differntial Equtations. 4. 671-696 (1999)

[文献書誌] Y. ADACHI, H. KADO,and T. SUZUKI: "Parameter descending method and the magnetoence phalography"Information. 2. 443-458 (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] Y. ISOZAKI and S. KOTANI: "Asymptotic estimates for the first hitting time of fluctuating addictive functionals on Browman motion"Seminar on Probability. (to appear).

[文献書誌] S. BENVENUTI and T. NISHTANI: "Necessary conditions for the hyperbolicity of 2×2 systems"Japanese J. Math.. 25. 377-408 (1999)

[文献書誌] F. COLOMBINI and T. SUZUKI: "Two by Two strongly hyperbolic systems and Gevreg classes"Ann. Mat. Univ. Ferrara. (to appear).

[文献書誌] A. MATSUMURA and M. MEI: "Convergence to travelling fronts of solutions of the p-system with viscosity in the presence of a boundary"Arch. Rational Mech. Anal.. 146. 1-22 (1999)

[文献書誌] A. MATSUMURA and K. NISHIHARA: "Global asymptotics toward rarefaction wave for solutions of the viscous p-system with boundary effect"Quart. Appl. Math.. (to appear).

[文献書誌] K. HIRACHI,G. KOMATSU and N. NAKAZAWA: "CR inovariants of weight five in the Bergman hernel"Adv. Math.. 143. 185-250 (1999)

[文献書誌] K. HIRACHI and G. KOMATSU: "Local Sobolev-Beryman kernels of stuctly pseudoconvex domains"Analysis acid Geometry on Several Complex Variables (Birk hauser). 63-96 (1999)

[文献書誌] 原澤隆一,四方順司,鈴木譲,今井秀樹: "楕円曲線暗号におけるMOV帰着とFR帰着の比較について"電子情報通信学会論文集A. 1278-1290 (1999)

[文献書誌] J. SUZUKI: "Learning Baysian belief networks based on the MDL principle : basic properties"IEI. CE Trans. on Foundamentals. 82A. (1999)

[文献書誌] J. SHIKATA,Y. ZHENG,J. SUZUKI,H. IMAI: "Realizing the Menezes-Okamoto-Vanstone (MOV) reduction efficiently for general alliptis curves"IEI. CE Trans. on Foundamentals. (to appear).

[文献書誌] A. MATSUO and K. NAGATOMO: "A note on free bosanic vertex algebra and its conformal vectors"J. Algebra. 212. 365-418 (1999)

[文献書誌] A. MATSO and K. NAGATOMO: "Axioms for vertex algebra and the locality of quantum fields"Memories of Math Soc. Japan. 4. (1999)

[文献書誌] M. MIKI.: "Toroidal and level O U^'_8 (<sl>^^^∧_<n+1>) actions on U_8(<gl>^^^∧_<n+1>) modules"J. Math. Phys.. 40. 3191-3210 (1999)

[文献書誌] A. Atsuji: "A Casorati -Weierstrass theorem for holomorphic maps invariant Q-field of helomorphic diffusions"Bull. Sci. Math.. 123. 371-383 (1999)

[文献書誌] A. Atsuji: "Remarks on harmoric maps into a core for stochastic complete manifolds"Proc. Japan Acad.. 75. 105-108 (1999)

[文献書誌] A. Atsuji: "A remark on a limiting behavior of the occupation times on unbounded domains of Browman motion"J. Math. Sci. University of Tokyo. (to appear).

[文献書誌] K. HIRACHI: "Construction of boundary onvariants and the logarithmic singularity of the Borgman kernel"Ann. Math.. (to appear).

[文献書誌] T. MORIOKA: "Regulari te de ondes Eastiques dans la reian Glancing des ondes P."Publ. RIMS. Kyoto Univ.. 35・4. 599-619 (1999)

[文献書誌] T. WADA: "A remark on long range scattering for the Hartree type eqation"Kyusyu J. Math.. (to appear).

[文献書誌] G. KOMATSU and M. KURANISHI(ed.): "Analysis and Geometry on Several Complex Variables Proceedings of 40 th Toniguchi Symposium"Birkkauser. (1999)

[文献書誌] 鈴木譲: "情報源符号化・無歪みデータ圧縮"培風館. (1999)

1999 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)