# American Institute of Mathematical Sciences

June  2003, 2(2): 211-231. doi: 10.3934/cpaa.2003.2.211

## Gevrey asymptotic theory for singular first order linear partial differential equations of nilpotent type — Part I —

 1 Graduate School of Mathematics, Nagoya University, Nagoya 464–8602, Japan

Received  May 2002 Revised  December 2002 Published  March 2003

This paper is concerned with the existence of the Gevrey asymptotic solutions for the divergent formal solution of singular first order linear partial differential equations of nilpotent type. By using the Gevrey version of Borel-Ritt's theorem, we can prove the existence of asymptotic solutions in a small sector unconditionally. However, when we require the Borel summability of the formal solution (that is, the existence of asymptotic solutions in an open disk), global analytic continuation properties for coefficients are demanded.
Citation: Masaki Hibino. Gevrey asymptotic theory for singular first order linear partial differential equations of nilpotent type — Part I —. Communications on Pure & Applied Analysis, 2003, 2 (2) : 211-231. doi: 10.3934/cpaa.2003.2.211
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