Investigations on Linear and Nonlinear Mathematical Analysis with Applications

关于非线性差分方程的研究研究了一阶或高阶非线性差分方程的解析解、解的存在性和渐近表示。我们希望确定这些方程的解流形的结构研究了一类边界条件和二类边界条件同时给定的三维平稳Stokes方程的非线性偏微分方程。用惩罚法研究了竖炉的自由边界问题，并进一步进行了数值处理。对对称截面的二维平衡等离子体进行了理论和数值研究。用一般牛顿法研究了莫泽型非线性演化方程。研究拟线性波动方程的柯西问题。我们将进一步研究全局解的存在性系统理论研究研究了具有无限维状态空间的线性动力系统。得到了细模空间存在的充分必要条件。

[1] Study on nonlinear difference equationsAnalytic solutions, their existency and asymptotic representations, are investigated for nonlinear difference equations of the first order or higher order. We wish to determine the structure of solution manifolds for these equations.[2] Study on nonlinear partial differential equations3-dimensional stationary Stokes equations are investigated when the boundary conditions of the first kind and of the second kind are given simultaneously. Free boundary problem in a shaft furnace is investigated with penalty method, and further treated numerically. 2-dimensional equilibrium plasma with symmetric cross section is investigated, both theoretically and numerically. Nonlinear evolution equations of Moser's type are investigated with the general Newton method. Cauchy problems for quasi-linear wave equations are investigated. Existency of global solutions will be further investigated.[3] Study on system theoryLinear dynamical systems with infinite dimensional state spaces are investigated. The necessary and sufficient conditions for the existence of fine moduli spaces are obtained.