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Asymptotic analytical study of differential equations

微分方程的渐近分析研究

基本信息

批准号：
15540186
负责人：
UCHIYAMA Koichi
金额：
$ 1.41万
依托单位：
Sophia University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2003
资助国家：
日本
起止时间：
2003 至 2004
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-15540186/
关键词：
asymptotic analysis Borel summable multi-summable Fuchsian equation totally characteristic A-elliptic distribution with support in a cone stochastic complexity 形式級数解 multi-summability 漸近展開確定特異点型非線形偏微分方程式正の定符号型超関数 nonlinear t

项目摘要

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.

A.内山用优级数方法证明了一类具有正则奇性的非线性偏微分方程的形式解的收敛性。Ouchi证明了一类半线性1阶奇异偏微分方程形式解的Borel可和<st>性及其在向量场规范形上的应用，以及一类常微分方程形式解的多重可和性. Tahara得到了Fuchsian非线性偏微分方程解的奇异性结构，一阶正规型偏微分方程奇异解存在的充要条件，以及全特征型非线性偏微分方程解的奇异性和唯一性的存在（不）性.真实的区域上微分方程的渐近分析及相关分析.Uchiyama证明了2阶一维p-椭圆型方程径向解的局部唯一性<nd>，并与L.Paredes一起从4阶p-椭圆型方程的一维模型中得到了一个具有正则奇异性的非线性偏微分方程的候选<th>解.吉野和M Suwa等对指数型分布进行了刻划及应用，得到了关于正定分布的一些结果.平田给出了3阶非线性偏微分方程通过椭圆函数的一族解的具体表示<rd>。后藤对渐近包含进行了研究。Aoyagi给出了非分析学习机的随机复杂性的渐近展开。