Study on differential equations by asymptotic analysis

A.复域上微分方程的渐近分析.S.Ouchi对一类含有Fuchsian线性偏微分方程得到了幂型奇异解的积分表示，并给出了解的渐近性态和Gevrey型估计.他还证明了multisummability正式解决方案的一类线性偏微分方程，他programmured。田原，与H。Chen和Z.Luo等，证明了关于空间变量的具有非正则奇异性的非线性偏微分方程形式解的Maillet型定理。他还获得了与J.洛佩尖锐的结果解析延续的解决方案一类非线性偏微分方程的正常类型。与H.Yamazawa一起，他确定了一类Fuchsian型非线性偏微分方程解的结构，而没有对特征指数附加条件。真实的域上微分方程的渐近分析及相关的应用分析.K.Uchiyama和L.Paredes利用复域上Briot-Bouquet型非线性常微分方程给出了一维p-椭圆方程在奇点附近解的解析表达式. K.Yoshino利用热传导方程解的渐近性态刻画了凸真锥上支撑的回火分布。松泽H.Hirata给出了热方程和波动方程的半线性Pintegro-Diffie插值的初值空间与非线性参数之间的关系。他还建造了具体的解决方案，由Backlund变换适用于平凡的解决方案，以一定的第三阶非线性偏微分方程。S.后藤研究了算子代数中的子因子，计算主图并对子因子进行分类。M.Aoyagi研究了有关三角形识别的数值算法，这是在分割3维障碍物后分割四面体后识别障碍物的必要条件。

A. Asymptotic analysis of differential equations in the complex domain.S.Ouchi obtained integral representations of solutions with singularities of power type for a class containing Fuchsian linear PDEs and gave asymptotic behavior of solutions and Gevrey type estimates. He also proved multisummability of formal solutions to a class of linear PDEs he conjectured. H.Tahara, with H. Chen and Z.Luo, proved theorems of Maillet type for formal solutions to nonlinear PDEs with irregular singularity respect to space variables. He also obtained with J. Lope a sharp result on analytic continuation of solutions to a class of nonlinear PDEs of normal type. With H.Yamazawa, he determined the structure of solutions to a class of nonlinear PDEs of Fuchsian type without additional conditions on characteristic exponents.B. Asymptotic analysis of differential equations in the real domain and related applied analysis.K.Uchiyama, with L.Paredes, gave analytic expressions of solutions near their singularities for a nonlinear ODE, one dimensional p-elliptic Eq, using nonlinear ODE of Briot-Bouquet type in the complex domain. K.Yoshino characterized tempered distributions with support contained in convex proper cone, by asymptotic behavior of solutions to the heat equation, after T. Matsuzawa. H.Hirata gave relation between nonlinear parameter and the initial value space of semilinear Pintegro-DifiE interpolating the heat equation and the wave equation. He also constructed concrete solutions by Backlund transformations applied to trivial solutions to a certain 3rd order nonlinear PDE. S.Goto studied subfactors in operator algebra to compute principal graphs and to classify subfactors. M.Aoyagi studied numerical algorithms concerning triangle recognition, necessary for recognition of obstacles as complex after division of tetraheds after division of 3-dim obstacles.