Geodesic
On the Goursat problem for a second order equation
Electronic journal of differential equations, Tome 2002 (2002)
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.
Classification : 35L20
Keywords: goursat problem, C^infty-wellposed 
@article{EJDE_2002__2002__a85,
     author = {Tarama,  Shigeo},
     title = {On the {Goursat} problem for a second order equation},
     journal = {Electronic journal of differential equations},
     year = {2002},
     volume = {2002},
     zbl = {1056.35108},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a85/}
}
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Tarama,  Shigeo. On the Goursat problem for a second order equation. Electronic journal of differential equations, Tome 2002 (2002). http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a85/