Proceedings of the American Mathematical Society

Author(s): Jaime Carvalho E Silva; Carlos Leal
Journal: Proc. Amer. Math. Soc. 125 (1997), 471-475.
MSC (1991): Primary 35L30, 35E15, 35G10
Retrieve article in: PDF
This article is available free of charge

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.

1.: J. Carvalho E. Silva, Problème de Goursat-Darboux ge\'{n}éralisé pour un ope\'{r}ateur du troisième ordre, Série I, no. 6, C. R. Acad. Sc. Paris, t. 303 (1986), 223-226. MR 87i:35033
2.: -, On the hyperbolicity of a third order operator and the generalized Goursat-Darboux problem, Portugaliae Mathematica, 46 Sup, 1989, pp. 567-577. CMP 91:04
3.: -, Asymptotic representations for some multiple hypergeometric functions, Publicações de Física-Matemática, no. 5, 1986, pp. 26-45.
4.: Y. Hasegawa, On the $C^{\infty }$ -Goursat problem for 2nd order equations with real constant coefficients, Proc. Japan Academy, vol. 51 (7), 1975, pp. 516-519. MR 52:14670
5.: Y. L. Luke, The special functions and their approximations-vol. 1, Academic Press, New York, 1969. MR 39:3039
6.: S. Mizohata, The theory of partial differential equations, Cambridge University Press, Cambridge, 1973. MR 58:29033
7.: J. Vaillant, Caractéristiques multiple set bicaractéristiques des systèmes d'équations aux dérivées partielles linéaires et à coefficients constants, Ann. Inst Fourier, vol. 15(2), 1965, pp. 225-311. MR 32:7919
8.: -, Données de Cauchy portées par une caractéristique double, dans le cas d'un système linéaire d'équations aux dérivées partielles; role des bicaractéristiques, J. Math. Pures et Appl., vol. 47, 1968, pp. 1-40. MR 38:6209

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 35L30, 35E15, 35G10

Jaime Carvalho E Silva
Affiliation: Departamento de Matemática, Universidade de Coimbra, Apartado 3008, 3000 Coimbra, Portugal
Email: jaimecs@mat.uc.pt

Carlos Leal
Affiliation: Departamento de Matemática, Universidade de Coimbra, Apartado 3008, 3000 Coimbra, Portugal
Email: carlosl@mat.uc.pt

DOI: 10.1090/S0002-9939-97-03684-8
PII: S 0002-9939(97)03684-8
Keywords: Goursat problem, Darboux problem, hypergeometric functions of several variables, third order operators.
Received by editor(s): August 11, 1995
Additional Notes: The first author was partially supported by CMUC-Coimbra and JNICT Project no.PMCT/C/CEN/18/90.
The second author was partially supported by CMUC-Coimbra.
Communicated by: Jeffrey B. Rauch
Copyright of article: Copyright 1997, American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support Help
ISSN 1088-6826 (e) ISSN 0002-9939 (p)

Previous issue \| Table of contents \| Next issue Articles in press \| Recently posted articles \| Most recent issue \| All issues Previous Article \| Next Article


	Comments: webmaster@ams.org © Copyright 2009, American Mathematical Society Privacy Statement		Search the AMS