The generalized Goursat-Darboux problem for a third order operator

Silva, Jaime; Leal, Carlos

doi:10.1090/S0002-9939-97-03684-8

The generalized Goursat-Darboux problem for a third order operator
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by Jaime Carvalho E Silva and Carlos Leal PDF

Proc. Amer. Math. Soc. 125 (1997), 471-475 Request permission

Abstract:

It is proved that if a generalized Goursat-Darboux problem is $C^{\infty }$-well posed then the operator cannot contain derivatives with respect to one of the variables.

References

Jaime Carvalho e Silva, Problème de Goursat-Darboux généralisé pour un opérateur du troisième ordre, C. R. Acad. Sci. Paris Sér. I Math. 303 (1986), no. 6, 223–226 (French, with English summary). MR 860822
—, On the hyperbolicity of a third order operator and the generalized Goursat-Darboux problem, Portugaliae Mathematica, 46 Sup, 1989, pp. 567–577.
—, Asymptotic representations for some multiple hypergeometric functions, Publicações de Física-Matemática, no. 5, 1986, pp. 26–45.
Yukiko Hasegawa, On the $C^{\infty }$-Goursat problem for 2nd order equations with real constant coefficients, Proc. Japan Acad. 51 (1975), no. 7, 516–519. MR 393862
Yudell L. Luke, The special functions and their approximations, Vol. I, Mathematics in Science and Engineering, Vol. 53, Academic Press, New York-London, 1969. MR 0241700
Sigeru Mizohata, The theory of partial differential equations, Cambridge University Press, New York, 1973. Translated from the Japanese by Katsumi Miyahara. MR 0599580
Jean Vaillant, Caractéristiques multiples et bicaractéristiques des systèmes d’équations aux dérivées partielles linéaires et à coefficients constants, Ann. Inst. Fourier (Grenoble) 15 (1965), no. fasc. 2, 225–311 (French). MR 190507
Jean Vaillant, Données de Cauchy portées par une caractéristique double, dans le cas d’un système linéaire d’équations aux dérivées partielles, rôle des bicaractéristiques, J. Math. Pures Appl. (9) 47 (1968), 1–40 (French). MR 237932