Electron. J. Diff. Eqns., Vol. 2002(2002), No. 52, pp. 1-28.

On the Goursat problem for a second order equation

Shigeo Tarama

We consider the Goursat problem for second order operators and show existence and uniqueness of smooth solutions. We prove one of the results of Hasegawa (J. Math. Soc. Japan 50 (1998), no. 3, 639--662) by the energy method. The same method is applied when one of the surfaces where the Goursat data are given is a non-characteristic.

Submitted October 23, 2001. Published June 6, 2002.
Math Subject Classifications: 35L20.
Key Words: Goursat problem, C^{\infty}-wellposed.

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Shigeo Tarama
Laboratory of Applied Mathematics, Faculty of Engineering,
Osaka City University, 558-8585 Osaka, Japan
e-mail: starama@mech.eng.osaka-cu.ac.jp
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