Asymptotic analytical study of differential equations

内山证明了一类具有正则奇异性的非线性偏微分方程解的形式解通过优级数方法收敛。Ouchi证明了一类半线性1^t；st&gt；阶奇异偏微分方程解的Borel可和性及其在向量场的标准型中的应用，并证明了一类被视为常微分方程组扰动的偏微分方程解的多重可和性.Tahara得到了Fuchsian非线性偏微分方程解的奇性结构，一阶正规型偏微分方程解存在奇性的充要条件，以及完全特征型非线性偏微分方程解的(非)奇性与唯一性。B.实域中微分方程解的渐近分析及相关分析。Uchiyama证明了一维p-椭圆型方程的径向解的局部唯一性，并与L.Paredes从4^>阶p-椭圆型方程的一维模型得到了一组具有正则奇性的非线性偏微分方程候选者。Yoshino和M.Suwa刻画了指数型分布及其应用，得到了关于正定分布的结果。Hirata给出了3^&lt；Rd&gt；阶非线性偏微分方程解的椭圆函数族的具体表示。后藤健二对渐近包含进行了研究。Ayagi给出了非解析学习机的随机复杂性的渐近展开式。

A. Asymptotic analysis of differential equations in complex domain.Uchiyama showed that formal solutions to a certain nonlinear PDE with regular singularity converge by the method of majorant series. Ouchi showed Borel summability of formal solutions to a certain semilinear 1^<st> order singular PDE and its application to normal form of vector fields and multi-summability of formal solution to a certain PDE regarded as perturbation of ODE. Tahara obtained the structure of singularities of solutions to Fuchsian nonlinear PDE, necessary or sufficient conditions for existence of singular solutions to 1St order PDE's of normal type and (non)existence of singularities and uniqueness of solutions to nonlinear PDE of totally characteristic type.B. Asymptotic analysis of differential equations in real domain and related analysis.Uchiyama showed local uniquness of radial solutions to 2^<nd> order one dimensional p-elliptic equations and obtained with L.Paredes a candidate of nonlinear PDEs with regular singularity from one dimensinal model of 4^<th> order p-elliptic equations. Yoshino, with M. Suwa, characterized distribution of exponential type with applications and obtained results on positive definite distribution. Hirata gave a concrete representation of a family of solutions through elliptic functions to 3^<rd> order nonlinear PDE. Goto did reserch on asymptotic inclusion. Aoyagi gave asymptotic expasion of the stochastic comlexity of non-analytic learning machines.