Singular solutions of the Briot-Bouquet type partial differential equations

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

In 1990, Gérard-Tahara [2] introduced the Briot-Bouquet type partial differential equation t∂tu = F(t, x, u, ∂ xu), and they determined the structure of singular solutions provided that the characteristic exponent ρ(x) satisfies ρ(0) ∉ {1, 2,...}. In this paper the author determines the structure of singular solutions in the case ρ(0) ∈ {1, 2,...}.

Original languageEnglish
Pages (from-to)617-632
Number of pages16
JournalJournal of the Mathematical Society of Japan
Volume55
Issue number3
Publication statusPublished - 2003 Jul
Externally publishedYes

Keywords

  • Characteristic exponent
  • Singular solution
  • The Briot-Bouquet type partial differential equations

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Singular solutions of the Briot-Bouquet type partial differential equations. / Yamazawa, Hiroshi.

In: Journal of the Mathematical Society of Japan, Vol. 55, No. 3, 07.2003, p. 617-632.

Research output: Contribution to journalArticle

@article{a9df8ca34dc84f10a951316a1d7d8c99,
title = "Singular solutions of the Briot-Bouquet type partial differential equations",
abstract = "In 1990, G{\'e}rard-Tahara [2] introduced the Briot-Bouquet type partial differential equation t∂tu = F(t, x, u, ∂ xu), and they determined the structure of singular solutions provided that the characteristic exponent ρ(x) satisfies ρ(0) ∉ {1, 2,...}. In this paper the author determines the structure of singular solutions in the case ρ(0) ∈ {1, 2,...}.",
keywords = "Characteristic exponent, Singular solution, The Briot-Bouquet type partial differential equations",
author = "Hiroshi Yamazawa",
year = "2003",
month = "7",
language = "English",
volume = "55",
pages = "617--632",
journal = "Journal of the Mathematical Society of Japan",
issn = "0025-5645",
publisher = "Mathematical Society of Japan - Kobe University",
number = "3",

}

TY - JOUR

T1 - Singular solutions of the Briot-Bouquet type partial differential equations

AU - Yamazawa, Hiroshi

PY - 2003/7

Y1 - 2003/7

N2 - In 1990, Gérard-Tahara [2] introduced the Briot-Bouquet type partial differential equation t∂tu = F(t, x, u, ∂ xu), and they determined the structure of singular solutions provided that the characteristic exponent ρ(x) satisfies ρ(0) ∉ {1, 2,...}. In this paper the author determines the structure of singular solutions in the case ρ(0) ∈ {1, 2,...}.

AB - In 1990, Gérard-Tahara [2] introduced the Briot-Bouquet type partial differential equation t∂tu = F(t, x, u, ∂ xu), and they determined the structure of singular solutions provided that the characteristic exponent ρ(x) satisfies ρ(0) ∉ {1, 2,...}. In this paper the author determines the structure of singular solutions in the case ρ(0) ∈ {1, 2,...}.

KW - Characteristic exponent

KW - Singular solution

KW - The Briot-Bouquet type partial differential equations

UR - http://www.scopus.com/inward/record.url?scp=0142086974&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0142086974&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0142086974

VL - 55

SP - 617

EP - 632

JO - Journal of the Mathematical Society of Japan

JF - Journal of the Mathematical Society of Japan

SN - 0025-5645

IS - 3

ER -