Integrated Studies towards New Development in Mathematical Sciences

数学科学新发展的综合研究

• 批准号: 07304017
• 负责人: MIURA Masayasu
• 金额: $ 3.9万
• 依托单位: University of Tokyo
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (A)
• 财政年份: 1995
• 资助国家: 日本
• 起止时间: 1995 至 1996
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-07304017/
• 关键词: Bifurcation theory of flow problems; Algorithm of parallel computing; Theooretical study of domain decomposition methods; Computer aided analysis; Methods to mathematical sciences; 数理科学的概論; Industrial Mathematics; 数理ファイナンス; ソフトサイエンス

Towards new development in mathematical sciences, we have considered mathematical understanding of several topics in engineering, natual sciences etc. For instance, Tabata and Okamoto have studied bifurcation theories, numerical algorithm, application to several concrete problems, parallel computing in large scale systems in fluid dynamics problems. Ikeda and Nishiura have analycally and complementarily numerically nvestigated to reveal the mecanism of phase seperation and interfacial problems in physical science, by using reaction-diffuison model systems. Mori, Kawarada and Mitsui have discussed mathemathematical topics arising in Industrial mathematics. Especially, they have developed new numerical algorithm of domain decomposition methods, which is known as one of effective scientific numerical methods. Nishida, Nakao and Tsutsumi have studied qualitative properites of nonlinear partial differential equations, from the numerical aided analysis standing point, and proposed a new analytical methods to understand nonlinear phenomena. Mimura and his group have discussed biological problems, especially aggregation, segregation of biological individuals described by reaction-diffusion systems, by integrating analytical methods, numerical simulations and visualization. This appraoch is a trial to develop new methods in mathematical sciences. The results obtained above were reperented in the meeting of Applied Mathematics in Japan which was held on December everyyear and published in the forms of proceedings.

为了数学科学的新发展，我们考虑了工程、自然科学等领域中几个主题的数学理解。例如，Tabata和Okamoto研究了分叉理论、数值算法、在几个具体问题中的应用、流体动力学问题中大系统的并行计算。Ikeda和Nishiura利用反应-扩散模型系统，对物理科学中的相分离机理和界面问题进行了分析和互补的数值研究。森，河原田和三井讨论了数学主题所产生的工业数学。特别是区域分解方法，他们发展了新的数值算法，被称为有效的科学数值方法之一。Nishida，Nakao和Tsutsumi从数值辅助分析的角度研究了非线性偏微分方程的定性性质，提出了一种新的分析方法来理解非线性现象。Mimura和他的团队通过整合分析方法，数值模拟和可视化来讨论生物学问题，特别是由反应扩散系统描述的生物个体的聚集和分离。该方法是数学科学中发展新方法的一次尝试。上述结果在每年12月举行的日本应用数学会议上以会议录的形式发表。

项目成果

M. Mimura etal: "Multi-dimentional transition layers for an exothermic reaction-diffusion system in long cylindrical domains" J. Math. Sci., Univ. Tokyo. (1996)

M. Mimura 等人：“长圆柱域中放热反应扩散系统的多维过渡层”J. Math。

Y. Nishiura: "Coexistence of infinitely many stable solutions to reaction-diffusion systems" Dynamics Report. 3. 25-103 (1994)

Y. Nishiura：“反应扩散系统无限多个稳定解的共存”动力学报告。

T. Nishida etal: "Eigenvalue problems of the parameter dependent system of ODEs computer aided proof"

T. Nishida 等人：“ODE 计算机辅助证明的参数相关系统的特征值问题”

I.Ohnishi and Y.Nishiura: "Spectral comparison between the second and the fourth order equations of conservative type with non-local terms" preprint series of Isaac Newton Institute for Mathematical Sciences.

I.Ohnishi 和 Y.Nishiura：“保守型二阶和四阶方程与非局部项的谱比较”艾萨克·牛顿数学科学研究所预印本系列。

M.Mimura and T.Tsujikawa: "Aggregating pattern dynamics in a chemotaxis model including growth" Physica A,. 230. 499-543 (1996)

M.Mimura 和 T.Tsujikawa：“包括生长在内的趋化模型中的聚合模式动态”Physica A，。