Éditeur(s) : HAL CCSD
Résumé : International audience
In this paper we investigate solutions to the semi-linear wave equation in canonical form with non Lipschitz non-linearity and distributions or other generalized functions as data. To give a meaning to the Goursat problem with irregular data, we replace it by a biparametric family of problems. The first parameter turns the problem into a family of Lipschitz problems, the second one regularizes the data. Finally, the problem is solved in an appropriate algebra. We show that the solution is equal to the non-regularized one. In the examples, we take advantage of our results to give a new approach of the blow-up problem.
Differential Equations & Applications

Droits : info:eu-repo/semantics/OpenAccess
hal-00345090
https://hal.archives-ouvertes.fr/hal-00345090
https://hal.archives-ouvertes.fr/hal-00345090v2/document
https://hal.archives-ouvertes.fr/hal-00345090/file/Devoue-Goursat-wellposed-12-08.pdf