Comptes Rendus
On the nonlinear type singularities for semilinear Cauchy problems
Comptes Rendus. Mathématique, Volume 335 (2002) no. 5, pp. 453-458.

We consider the Cauchy problem for the semilinear wave equation. The Cauchy data are assumed to be conormal with respect to a point, and the source term is polynomial with respect to the solution and its first derivatives. Thanks to the study of multiplicative properties of some refined hyperbolic conormal spaces, we improve the known results about the nonlinear type singularities of the solution.

On considère le problème de Cauchy pour l'équation des ondes semi-linéaire à données de Cauchy conormales par rapport à un point, et à terme source polynomial par rapport à la solution et à ses dérivées premières. Grâce à l'étude des propriétés multiplicatives d'espaces conormaux hyperboliques précisés, on améliore les résultats connus sur la taille des singularités de type non-linéaire de la solution.

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Accepted:
Published online:
DOI: 10.1016/S1631-073X(02)02497-4

Daoyuan Fang 1; Gilles Laschon 2; Alain Piriou 3

1 Department of Mathematics, Zhejiang University, Hangzhou 310027, PR China
2 IUT d'Orsay, Université Paris Sud, plateau du Moulon, 91400 Orsay, France
3 Laboratoire J. A. Dieudonné, Université de Nice-Sophia-Antipolis, UMR n
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Daoyuan Fang; Gilles Laschon; Alain Piriou. On the nonlinear type singularities for semilinear Cauchy problems. Comptes Rendus. Mathématique, Volume 335 (2002) no. 5, pp. 453-458. doi : 10.1016/S1631-073X(02)02497-4. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02497-4/

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