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Comptes Rendus Mathématique
Volume 341, n° 1
pages 15-20 (juillet 2005)
Doi : 10.1016/j.crma.2005.05.002
Received : 22 February 2005 ;  accepted : 10 May 2005
Problèmes de Goursat pour des systèmes semi-linéaires hyperboliques
Goursat problems for some semilinear hyperbolic systems
 

Duplex Elvis Houpa a , Marcel Dossa b
a Faculté des sciences, université de Ngaoundéré, B.P. 454, Ngaoundéré, Cameroun 
b Faculté des sciences, université de Yaoundé I, B.P. 812, Yaoundé, Cameroun 

Résumé

Pour des systèmes dʼéquations semi-linéaires hyperboliques du second ordre à données initiales sur la réunion de deux hypersurfaces caractéristiques sécantes, et sous des hypothèses de structure assez générales sur les termes non linéaires, on montre dans un cadre dʼespaces de type Sobolev que la solution du problème de Goursat semi-linéaire ainsi posé est définie non seulement dans un voisinage assez petit de la sécante des deux hypersurfaces mais aussi dans un voisinage de la réunion toute entière de ces deux hypersurfaces. Pour citer cet article : D.E. Houpa, M. Dossa, C. R. Acad. Sci. Paris, Ser. I 341 (2005).

The full text of this article is available in PDF format.
Abstract

For some semilinear hyperbolic systems of the second order with initial data on two intersecting characteristic hypersurfaces, and under a general hypothesis on the structure of the nonlinear terms, we prove that the solution of the so-called semilinear Goursat problem is defined, not only on a small neighbourhood of the intersection of these hypersurfaces, but also in a neighbourhood of the entire union of the hypersurfaces. To cite this article: D.E. Houpa, M. Dossa, C. R. Acad. Sci. Paris, Ser. I 341 (2005).

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