Mathematical Analysis for Partial Differential Equations Arising in Mathematical Sciences

数学科学中出现的偏微分方程的数学分析

• 批准号: 11440055
• 负责人: SUJUKI Takoshi
• 金额: $ 7.62万
• 依托单位: Osaka University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B).
• 财政年份: 1999
• 资助国家: 日本
• 起止时间: 1999 至 2000
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-11440055/
• 关键词: chams taxis; free energy; blow-up; quantization; localization; collapse; Langevin equation; Fokker-Pharck equation; 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

We have extensive developments in analytic thoarees on the equations of magretoencaphalography and chamotaxis, For the system of sell-interacting particles we have made the relations clearer between the stochastic differential equation with the terms of friction and fluctuations, (that is, the Langerin equation) the Fokker-Planck equation under the treatment of statistical mechanics, (the is, the kinetic model) parabolic-elliptic system of chemolakis, semilinear elliptic boundary value problems with the exponential nonlinearity, and the system of gradiont flows. We have showed that those systems are to be indicated as the quantization of blow-up mechanism. In particular, we have proven analytically that the collapses are quantiged in the system of chemataxis.

本文对磁光晕和趋时性方程的分析理论作了广泛的发展。对于自相互作用粒子系统，我们使带有摩擦项和涨落项的随机微分方程之间的关系更加清楚，（即朗格林方程）统计力学处理下的福克-普朗克方程，（即动力学模型）抛物-椭圆方程组，具有指数非线性项的半线性椭圆边值问题，梯度流方程组。我们证明了这些系统可以用爆破机制的量子化来表示。特别是，我们已经证明了分析的崩溃是量化的系统中的chemataxis。

项目成果

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

S. BENVENUTI 和 T. NISHTANI：“2×2 系统双曲性的必要条件”Japan J. Math.. 25. 377-408 (1999)

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)

Ryuichi Harazawa、Junji Shikata、Joe Suzuki、Hideki Imai：“椭圆曲线密码学中 MOV 和 FR 约简的比较” IEICE Transactions A. 1278-1290 (1999)

A.Kohda and T.Suzuki: "Blow-up criteria for semilnear parabolic equations"J.Math.Anal.Appl.. 243. 127-139 (2000)

A.Kohda 和 T.Suzuki：“半线性抛物线方程的放大准则”J.Math.Anal.Appl.. 243. 127-139 (2000)

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

T.Senba 和 T.Suzuki：“数学生物学的抛物线-椭圆系统中的 cpomotaitic 崩溃”Adr.Differential Equrtions。

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

Y. NAITO 和 T. SUZUKI：“半线性热方程自相似解的激进对称性”J。