Applied and numerical analysis of nonlinear problems arising in the industry

工业中出现的非线性问题的应用和数值分析

• 批准号: 09640294
• 负责人: NAKAMURA Masaaki
• 金额: $ 1.86万
• 依托单位: Nihon University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1997
• 资助国家: 日本
• 起止时间: 1997 至 1999
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09640294/
• 关键词: MHD system; EOM system; PVM; phase separation; Lindley process; third order equation; unbounded solution; stability; 江口・沖・松村系; simulation; 無限精度; Phase sepatation; attractor; spinodal decomposition; stability; EOM system; Magneto-hydrodynam

In the term of the project (three years) many results are obtained. Important results are shown as follows.1. Uniqueness of the unbounded classical solution of the MHD system.We obtain the uniqueness of the unbounded classical solution of the MHD system under suitable conditions on asymptotic behaviors, MHD system is the basis of the magnetic Benard problem which we have been studying in these years.2. Mathematical and numerical analysis of Eguchi-Oki-Matsumura system.We introduced the mathematical formulation of the EOM system and show the existence results. We made the numerical simulation of the one- dimmensional system and obtained the stability of the constant solutions.3. Analysis of the third order equation.We obtain the non-existence of the monotone solution of the third order equation arising in the phenomena of the liquid crysta, which has the close relation to Kuramoto-Shivashinsky equation.4. Analysis of the complex system in the social science.(a) We analyzed the reversibility of the Lindley process with discrete states.(b) We determined the optimal inter-arrival times for the queuing system GI/GI/M/1.5. Development of the fast numerical computation and its application.We developed methods of fast numerical computations in the environment of the parallel computing offered by PVM. These methods enables the large-scaled numerical simulation of fluid mechanics.6. We held the international symposiums and domestic symposiums, for example, Fourth Japan-Chine joint seminar on numerical mathematics, DDM12 and RIMS symposiums. We joined the several international symposiums and presented our results.

在项目期间（三年）取得了许多成果。重要结果如下：1。MHD系统无界经典解的唯一性。在渐近行为的适当条件下，我们得到了MHD系统无界经典解的唯一性，MHD系统是我们近年来研究的磁贝纳德问题的基础。Eguchi-Oki-Matsumura系统的数学与数值分析。我们引入了EOM系统的数学公式，并给出了存在性结果。对一维系统进行了数值模拟，得到了常解的稳定性。三阶方程的分析。得到了液晶现象中出现的三阶方程单调解的不存在性，这与Kuramoto-Shivashinsky方程有密切的关系。社会科学中的复杂系统分析。(a)分析离散状态下Lindley过程的可逆性。(b)我们确定了排队系统GI/GI/M/1.5的最优到达时间。快速数值计算的发展及其应用。我们开发了在PVM提供的并行计算环境下的快速数值计算方法。这些方法使大规模的流体力学数值模拟成为可能。我们举办了国际研讨会和国内研讨会，如第四届中日数值数学联合研讨会，DDM12和RIMS研讨会。我们参加了几个国际研讨会，并介绍了我们的研究结果。

项目成果

T, Hanada, M.Nakamura and C.Shima: "Numerical analysis of E.O.M. Model"京都大学数理解析研究所講究録. 1129. (2000)

T、Hanada、M.Nakamura 和 C.Shima：“E.O.M. 模型的数值分析”京都大学数学科学研究所 Kokyuroku 1129。（2000 年）

N.Ishimura and M.Nakamura: "On the finite determination of the solution for the MHD equations"GAKUTO International Series, Mathematical Sciences and Applications, Recent Development in Domain Decomposition Methods and Flow Problems. 11. 136-144 (1998)

N.Ishimura 和 M.Nakamura：“关于 MHD 方程解的有限确定”GAKUTO 国际系列，数学科学与应用，域分解方法和流问题的最新进展。

Eds.H.Kawarada, M.Nakamura and C.Z.Shi: "Advances in numerical mathematics in Japan and China : the fourth Japan China joint-seminar on numerical mathematics"Gakko Tosho. 200 (1999)

Eds.H.Kawarada、M.Nakamura 和 C.Z.Shi：“日本和中国数值数学的进展：第四届日中数值数学联合研讨会”Gakko Tosho。

H. Osawa and C. Shima: "Reversibility of Lindley Processes with Discrete States"Report of the Research Institute of Science and Technology, Nihon University. 44. 1-8 (1999)

H. Osawa 和 C. Shima：“Reversibility of Lindley Processes with Discrete States”日本大学科学技术研究所的报告。

Mori et al (eds): "Recent Development in Domain Decomposition Method and Flow Problems,(予定)" Gakuto International Series,Mathematical Sciences and Applications vol.11,Gakko Tosho,Tokyo,1998., 約230 (1998)

Mori 等人（编）：“域分解方法和流问题的最新发展，（计划）”Gakuto International Series，数学科学与应用第 11 卷，Gakko Tosho，东京，1998 年，约 230（1998 年）