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Solutions globales de certaines équations de Fuchs non linéaires dans les espaces de Gevrey


Author: Faiza Derrab
Journal: Proc. Amer. Math. Soc. 135 (2007), 1803-1815
MSC (2000): Primary 35A05; Secondary 35G20, 35A20
Published electronically: December 28, 2006
MathSciNet review: 2286091
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Abstract | References | Similar Articles | Additional Information

Abstract: We consider nonlinear partial differential equations with several Fuchsian variables of type $ a(t,D_{t}) u(t,x) = f(t,x,Du(t,x))$, where $ a(t,D_{t})$ is a Fuchsian principal part of weight zero. We prove existence and uniqueness of a global solution to this problem in the space of holomorphic functions with respect to the Fuchsian variable $ t$ and in Gevrey spaces with respect to the other variable $ x$. The method of proof is based on the application of the fixed point theorem in some Banach algebras defined by majorant functions that are suitable to this kind of equation.


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Additional Information

Faiza Derrab
Affiliation: 86, Avenue Lieutenant Khelladi, 22000 Sidi-Bel-Abbès, Algérie
Email: nouveaucompte2003@yahoo.fr

DOI: https://doi.org/10.1090/S0002-9939-06-08670-9
Keywords: Nonlinear Fuchsian partial differential equation, several Fuchsian variables, global solution, Gevrey classes, method of majorants, fixed-point theorem.
Received by editor(s): March 4, 2005
Received by editor(s) in revised form: February 6, 2006
Published electronically: December 28, 2006
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.