Cauchy problem in entire function spaces. (Problème de Cauchy caractéristique à solution entière.) (French) Zbl 0984.35004

Pongérard, Patrice

J. Math. Sci., Tokyo 8, No. 1, 89-105 (2001).

Summary: For a Fuchsian differential operator with order \(m\) and weight \(p\in[0,m]\) in the sense of M. S. Baouendi and C. Goulaouic [Commun. Pure Appl. Math. 26, 455-475 (1973; Zbl 0256.35050)], we approach the study of the Cauchy problem in entire functions spaces. This article is mainly based on the fixed point theorem in a Banach space defined by a majorant function with two variables that is suitable to this kind of operator. The proposed method allows one to generalize a H. Yamane theorem and to give the order of the solution; when \(p=m\), we find again the well-known theorems.

MSC:

35A10	Cauchy-Kovalevskaya theorems
35A20	Analyticity in context of PDEs
35A05	General existence and uniqueness theorems (PDE) (MSC2000)

Keywords:

entire functions spaces; fixed point theorem