Singular solutions of nonlinear partial differential equations with resonances

Masafumi Yoshino; Akira Shirai

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Singular solutions of nonlinear partial differential equations with resonances

机译：具有共振的非线性偏微分方程的奇异解

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摘要

We present a Frobenius type theorem for a system of nonlinear partial differential equations. Typical application is the normal form theory of a singular vector field. The construction of a singular solution is closely related with a Riemann-Hilbert factorization.

机译：我们为非线性偏微分方程组提出Frobenius型定理。典型应用是奇异矢量场的范式理论。奇异解的构造与Riemann-Hilbert分解密切相关。

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来源
《Journal of the Mathematical Society of Japan》 |2008年第1期|p.237-263|共27页
作者
Masafumi Yoshino; Akira Shirai;
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收录信息美国《科学引文索引》(SCI);
原文格式 PDF
正文语种 eng
中图分类数学;
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专利

1. On the singular solutions of nonlinear singular partial differential equations I [J] . Hidetoshi Tahara Journal of the Mathematical Society of Japan . 2001,第3期

机译：关于非线性奇异偏微分方程I的奇异解
2. An Analytical and Approximate Solution for Nonlinear Volterra Partial Integro-Differential Equations with a Weakly Singular Kernel Using the Fractional Differential Transform Method [J] . Rezvan Ghoochani-Shirvan, Jafar Saberi-Nadjafi, Morteza Gachpazan International Journal of Differential Equations . 2018,第1期

机译：分数阶微分方程的非线性奇异核Volterra偏微分方程的解析和近似解
3. An Analytical and Approximate Solution for Nonlinear Volterra Partial Integro-Differential Equations with a Weakly Singular Kernel Using the Fractional Differential Transform Method [J] . Rezvan Ghoochani-Shirvan, Jafar Saberi-Nadjafi, Morteza Gachpazan International Journal of Differential Equations . 2018,第期

机译：使用分数差分变换法用弱奇异核的非线性Volterra部分积分差分方程的分析与近似解
4. Positive Solutions of Singular Integro-differential Equations at Resonance in Banach Spaces [C] . Jianxin Cao, Haibo Chen Machine vision, image processing, and pattern analysis . 2011

机译：Banach空间中共振奇异积分-微分方程的正解
5. High-order solution of elliptic partial differential equations in domains containing conical singularities [D] . Li, Zhiyi. 2009

机译：圆锥奇异域中椭圆偏微分方程的高阶解
6. Delayed singularity formation for solutions of nonlinear partial differential equations in higher dimensions [O] . Fritz John 1976

机译：高维非线性偏微分方程解的延迟奇异性形成。
7. Singular solutions of nonlinear partial differential equations with resonances [O] . Akira SHIRAI, Masafumi YOSHINO 2008

机译：具有共振非线性偏微分方程的奇异解
8. Singularities and symmetries of nonlinear ordinary and partial differential equations. Technical report, May 15, 1993--May 14, 1994 [R] . 1994

机译：非线性常微分方程的奇性和对称性。技术报告，1993年5月15日 - 1994年5月14日

Singular solutions of nonlinear partial differential equations with resonances

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