Applied and numerical analysis of nonlinear problems arising in the industry

在该项目的期限（三年）内，取得了许多成果。主要结果如下：1. MHD系统无界经典解的唯一性在适当的渐近性态条件下，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Benard问题的基础. Eguchi-Oki-Matsumura系统的数学和数值分析。我们介绍了EOM系统的数学形式，并给出了存在性结果。对一维系统进行了数值模拟，得到了常数解的稳定性.对三阶方程进行了分析，得到了液晶现象中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)我们分析了具有离散态的Lindley过程的可逆性。(b)我们确定了GI/GI/M/1.5排队系统的最佳到达间隔时间。快速数值计算及其应用的发展在PVM提供的并行计算环境下，我们发展了快速数值计算的方法。这些方法使流体力学的大规模数值模拟成为可能.我们举办了国际研讨会和国内研讨会，如第四届日中数值数学联合研讨会，DDM 12和RIMS研讨会。我们参加了几次国际研讨会，并介绍了我们的成果。

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.