Electron. J. Diff. Eqns., Vol. 2002(2002), No. 52, pp. 1-28.
### On the Goursat problem for a second order equation

Shigeo Tarama

**Abstract:**

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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