Mathematical Studies of singularities governed by nonlinear phenomena

非线性现象控制的奇点的数学研究

• 批准号: 08404005
• 负责人: MIURA Masayasu
• 金额: $ 26.05万
• 依托单位: Hiroshima University (1998-1999)The University of Tokyo (1996-1997)
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (A)
• 财政年份: 1996
• 资助国家: 日本
• 起止时间: 1996 至 1999
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-08404005/
• 关键词: Singular limit methods; Singular perturbation methods; Mean curvature equations; Mathematics of blow up phenomenon; Free boundary problem; Pattern formation; Numerical analysis of singularities; interfacial dynamics; パターン形式; 曲率方程式; 数値分岐理論; 生体系モ

Towards understanding of nonlinear phenomena, we have analytically and complementarily numerically investigated singularities governed by these phenomena from different aspects in mathematics. Since the head investigator had moved from University of Tokyo to Hiroshima University from the second year of the research plan, the original members of investigators had to be altered but we have achieved the purpose of the proposed research. Mimura has been continuously studied pattern formation arising in reaction-diffusion systems. In particular, he has developed singular limit methods to understand dynamics of such patterns, Ueyama numerically studied this problem. Sakamoto has considered singular perturbation procedures to establish the theory of internal layers in higher dimensions. Matano has investigated qualitative properties of solutions of reaction-diffusion systems by using the theory of infinite dimensional dynamical systems. Nagai has discussed the qualitative properties of blow u … More p problem, which is one of the singularities arising in nonlinear diffusion systems. For the development of basic singularity theories in mathematics. Kohno, Shishikura and Kubo have respectively developed theories of geometry and complex dynamical systems. Oharu has developed the nonlinear semi group theory of evolutional equations. Tokihiro has discussed the methods of super discriminations and has revealed the relation between cell automaton and the related differential equations. Yamamoto has established the theoretical frame work of inverse problems which are one of the singular problems of partial differential equations. Yanagida and Kimura have studied analytically and numerically mean curvature equations. On the other hand, from application viewpoints. Inaba has considered epidemic models arising in mathematical demography. Mimura and Sakaguchi have given the theoretical implication on diversity of spatial pattern arising in biological systems by the analysis of mathematical models. Yamada and Hayashi have carried out large scale computer simulations to understand earth circulation phenomenon. The above results have been reported in several conferences inside and outside of Japan. Most of them were talked at the Applied Mathematics Meeting in Japan which was held every year and were published in their proceedings. Less

为了理解非线性现象，我们从数学的不同方面对这些现象所控制的奇点进行了分析和补充数值研究。由于研究计划的第二年起，首席研究员从东京大学调到了广岛大学，原来的研究人员成员也发生了变化，但我们已经达到了拟定研究的目的。 Mimura 一直在不断研究反应扩散系统中出现的图案形成。特别是，他开发了奇异极限方法来理解这种模式的动力学，上山对这个问题进行了数值研究。坂本考虑了奇异扰动程序来建立更高维度的内层理论。 Matano 利用无限维动力系统理论研究了反应扩散系统解的定性性质。 Nagai 讨论了 Blow u … More p 问题的定性性质，该问题是非线性扩散系统中出现的奇点之一。发展数学中的基本奇点理论。河野、狮子仓和久保分别发展了几何和复杂动力系统理论。 Oharu 发展了演化方程的非线性半群论。 Tokihiro讨论了超判别方法，并揭示了元胞自动机与相关微分方程之间的关系。山本建立了偏微分方程奇异问题之一的反问题的理论框架。 Yanagida 和 Kimura 研究了解析和数值平均曲率方程。另一方面，从应用的角度来看。稻叶考虑了数学人口统计学中出现的流行病模型。 Mimura和Sakaguchi通过数学模型的分析给出了生物系统中空间格局多样性的理论含义。山田和林进行了大规模计算机模拟来了解地球环流现象。上述结果已在日本国内外的多个会议上报道。他们中的大多数在每年举行的日本应用数学会议上发表了演讲，并发表在他们的论文集中。较少的

项目成果

M.Mimura: "Aggregating pattern dymnamics in a chemotaxis model including growth"Physica A. 230. 499-543 (1996)

M.Mimura：“包括生长在内的趋化模型中的聚合模式动力学”Physica A. 230. 499-543 (1996)

M. Mimura: "Non-annihilation of traveling pulses in reaction-diffusion systems"J. Methods Appl. of Anal.. (in press). (2000)

M. Mimura：“反应扩散系统中行进脉冲的不湮灭”J。

H. Matano: "The global attractor of semilinear parabolic equations on SィイD21ィエD2"Discrete and Dynamical Systems. 3. 1-14 (1997)

H. Matano：“离散和动力系统上半线性抛物线方程的全局吸引子。3. 1-14 (1997)

I.Kubo: "White noise analysis associated with sequences of umnbers"Infinite Dimensional Analysis. 12・3. 315-336 (1999)

I.Kubo：“与数字序列相关的白噪声分析”无限维分析12・3（1999）。

I. Kubo: "White noise analysis associated with sequences of numbers."Infinite Dimensional Analysis. 12・3. 315-336 (1999)

I. Kubo：“与数字序列相关的白噪声分析”。无限维分析 12・3（1999）。