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Theses

Sur les singularités de certains problèmes différentiels

Abstract : In this thesis, we propose a method to solve some Cauchy problems with irregular or characteristic data by using the recent theories of generalized functions. We study a regular Cauchy problem and a regular Goursat problem in the first part with data on a monotonic curve. The second part is devoted to the setting up of an algebra adapted to the generalized Cauchy problem. In the third part, we give a meaning to a generalized Cauchy problem and we show that the problem admits a unique solution. We study a generalized Goursat problem in the same way. In the fourth part, we approach a characteristic Cauchy problem by a family of non-characteristic ones. The family of solutions is a representative of a generalized function we consider as the generalized solution of the problem in an appropriate algebra. We give a meaning to the characteristic Cauchy problem with irregular data by replacing it by a family of non-characteristic problems in an appropriate biparametric algebra. The first parameter permits to replace the given problem by a non-characteristic one, whereas the second parameter makes it regular. The family of solutions is a representative of a generalized function considered as the solution of the problem.
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https://tel.archives-ouvertes.fr/tel-00012098
Contributor : Victor Devoue <>
Submitted on : Tuesday, January 2, 2007 - 5:14:29 PM
Last modification on : Wednesday, July 18, 2018 - 8:11:26 PM
Long-term archiving on: : Friday, November 25, 2016 - 1:22:02 PM

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  • HAL Id : tel-00012098, version 2

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Victor Devoue. Sur les singularités de certains problèmes différentiels. Mathématiques [math]. Université des Antilles-Guyane, 2005. Français. ⟨tel-00012098v2⟩

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