A singular Cauchy problem for the Euler-Poisson-Darboux equation

作者：Watanabe Takuya^*; Urabe Jiichiroh

来源：Journal de Mathematiques Pures et Appliquees, 2010, 93(3): 223-239.

DOI：10.1016/j.matpur.2009.11.008

• Singular Cauchy problem
• Hypergeometric function
• Monodromy theory

We consider a singular Cauchy problem for the Euler-Poisson-Darboux equation of Fuchsian type in the time variable with ramified Cauchy data. In this paper we establish an expansion of the solutions in a series of hypergeometric functions and then investigate the nature of the singularities of the solutions.

• 出版日期2010-3