A STUDY OF SINGULARITIES IN NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS IN THE COMPLEX DOMAIN

复域非线性偏微分方程奇异性的研究

• 批准号: 19540197
• 负责人: TAHARA Hidetoshi
• 金额: $ 2.66万
• 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: 2007
• 资助国家: 日本
• 起止时间: 2007 至 2009
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-19540197/
• 关键词: 関数方程式; 偏微分方程式; 複素領域; 特異点; 形式解; 正則性; 合成積方程式; 正則解; 変換の方程式

We studied singularities of solutions of nonlinear partial differential equations in the complex domain, and obtained the following results. (1) In the case of Briot-Bouquet type partial differential equations, we determined all solutions which have singularities on a hypersurface. (2) We proved a sharp form of the uniqueness of the solution of nonlinear totally characteristic type partial differential equations, which yields the non-existence of singularities. (3) We constructed solutions with logarithmic singularities to certain nonlinear partial differential equations. (4) We determined asymptotic expansions of solutions of nonlinear partial differential equations of non-Kowalewskian type by using Mellin transformations.

研究了非线性偏微分方程在复域上解的奇异性，得到了以下结果：(1)对于Briot-Bouquet型偏微分方程，我们确定了在超曲面上具有奇点的所有解。(2)证明了非线性全特征型偏微分方程解的唯一性的一种尖锐形式，从而得到了奇异性的不存在性。(3)构造了一类非线性偏微分方程的对数奇异解。(4)利用Mellin变换确定了非kowalewski型非线性偏微分方程解的渐近展开式。

项目成果

A proof of Paley-Wiener theorem for Fourier hyperfunctions with support in a proper convex cone by the heat kernel method.

通过热核方法在真凸锥的支持下证明傅里叶超函数的 Paley-Wiener 定理。

• 发表时间: 2008
• 期刊: Complex Var. Elliptic Equ. 53
• 作者: Ide Takanori;Isozaki Hiroshi;Nakata Susumu;Siltanen Samuli;高橋泰嗣;Kakehi Tomoyuki;高橋泰嗣;H.Tahara;Kakehi Tomoyuki;高橋泰嗣;Hidetoshi Tahara;筧 知之;高橋泰嗣;Kakehi Tomoyuki;Hidetoshi Tahara-Hideshi Yamane;高橋泰嗣;Kakehi Tomoyuki;Hidetoshi Tahara;高橋泰嗣;Sunao Ouchi;高橋泰嗣;Kunio Yoshino-Yasuyuki Oka;N. Mizoguchi;亀山敦;M. Kato;Masanori Suwa-Kunio Yoshino
• 通讯作者: Masanori Suwa-Kunio Yoshino

非線型偏微分方程式と対数的特異性

非线性偏微分方程和对数奇异性

• 发表时间: 2008
• 作者: M. Fila;J. R. King;M. Winkler and E. Yanagida;高橋 泰嗣;H. Tahara;N. Mizoguchi;Y.Shibata and S.Shimizu;田村 高幸;田原秀敏;N. Mizoguchi;Y.Shibata and S.Shimizu;H. Tahara;高橋 泰嗣;田原秀敏;N. Mizoguchi;Y.Shibata and S.Shimizu;H. Tahara;高橋 泰嗣;Y.Shibata and S.Shimizu;N. Mizoguchi;Hidetoshi Tahara;高橋 眞映;Koji Kikuchi;N. Mizoguchi and T. Senba;加藤 幹雄;H. Tahara;菊地光嗣;N. Mizoguchi;田原秀敏;菊地光嗣;N. Mizoguchi;田原秀敏;N. Mizoguchi;菊地光嗣;山根英司-田原秀敏;菊地光嗣;N. Mizoguchi;山根英司-田原秀敏
• 通讯作者: 山根英司-田原秀敏

Coupling of Two Partial Differential Equations and its Application, II : the Case of Briot-Bouquet Type PDEs

• DOI: 10.2977/prims/1241553125
• 发表时间: 2009-06
• 期刊: Publications of The Research Institute for Mathematical Sciences
• 影响因子: 1.2
• 作者: H. Tahara

Coupling of two partial differential equations and its application. Algebraic Analysis of Differential Equations (edited by T. Aoki, H. Majima, Y. Takei and N. Tose)

两个偏微分方程的耦合及其应用。

• 发表时间: 2008
• 期刊: Springer
• 作者: Ide Takanori;Isozaki Hiroshi;Nakata Susumu;Siltanen Samuli;高橋泰嗣;Kakehi Tomoyuki;高橋泰嗣;H.Tahara;Kakehi Tomoyuki;高橋泰嗣;Hidetoshi Tahara;筧 知之;高橋泰嗣;Kakehi Tomoyuki;Hidetoshi Tahara-Hideshi Yamane;高橋泰嗣;Kakehi Tomoyuki;Hidetoshi Tahara
• 通讯作者: Hidetoshi Tahara

On a reduction of Briot-Bouquet type partial differential equations in a resonant case.

关于谐振情况下 Briot-Bouquet 型偏微分方程的简化。

• 发表时间: 2008
• 作者: M. Iida;K. Nakashima and E. Yanagida;高橋泰嗣;Hidetoshi Tahara
• 通讯作者: Hidetoshi Tahara