Electronic Journal of Differential Equations,
Vol. 2002(2002), No. 52, pp. 1-28.

Title: On the Goursat problem for a second order equation

Author: Shigeo Tarama (Osaka City Univ., Japan)
         
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.