Singularities of solutions of the Fuchsian Cauchy problem with ramified data

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:406

Article

Watanabe, Takuya¹  Urabe, Jiichiroh² 

[1] Ritsumeikan Univ, Dept Math Sci, Kusatsu, Shiga 5258577, Japan

[2] Doshisha Univ, Fac Culture & Informat Sci, Kyotanabe, Kyoto 6100394, Japan

关键词: Singular Cauchy problem;    Fuchsian partial differential equations;    Propagation of singularities;    Characteristics;   

DOI  :  10.1016/j.jmaa.2013.04.049

来源: Elsevier

【 摘 要 】

We concretely construct the solution of the singular Cauchy problem for a Fuchsian partial differential operator of weight one by means of hypergeometric representations and study what kind of singularities appear on the characteristic surfaces determined by the principal part of the operator. In particular we investigate how the singularities are characterized not only by the principal part but also by the subprincipal part restricted at the origin and the ramification index of Cauchy data. (C) 2013 Elsevier Inc. All rights reserved.

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