On the Goursat problem in the Gevrey class for some second order equations

The Goursat problem for certain types of second order linear equations is considered. The Goursat problem for those second order equations is not \mathscr{E} -wellposed in general. For a certain type homogeneous equations, the Goursat problem is \mathscr{E} -wellposed. Necessary or sufficient condit...

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Bibliographic Details
Published in:Journal of the Mathematical Society of Japan 2003-07, Vol.55 (3), p.669-679
Main Author: HASEGAWA, Yukiko
Format: Article
Language:English
Subjects:
35M10
35M99
Gevrey class
Goursat problem
wellposedness
Online Access:Get full text
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Summary:The Goursat problem for certain types of second order linear equations is considered. The Goursat problem for those second order equations is not \mathscr{E} -wellposed in general. For a certain type homogeneous equations, the Goursat problem is \mathscr{E} -wellposed. Necessary or sufficient conditions on lower order terms for \mathscr{E} -wellposedness are given. Wellposedness in Gevrey class is discussed.
ISSN:0025-5645
1881-2333
DOI:10.2969/jmsj/1191418996