Generalized solutions of singular differential problems. Relationship with classical solutions

Antoine Delcroix; Victor Devoue; Jean-André Marti

doi:10.1016/j.jmaa.2008.11.077

Journal articles

Generalized solutions of singular differential problems. Relationship with classical solutions

Antoine Delcroix ^{1, 2} Victor Devoue ³ Jean-André Marti ³

1 CRREF - Centre de recherches et de ressources en éducation et formation

2 AOC - Analyse Optimisation Controle

3 CEREGMIA - Centre de Recherche en Economie, Gestion, Modélisation et Informatique Appliquée

Abstract : We discuss various methods of regularization of singular differential problems. Their common point is that we use the flexibility of the theories of nonlinear generalized functions for adapting the regularization to the singularity of the problem. We particularly underline the relationship between the generalized solutions and those classical or distribution, when they exist, giving a general result for the case of the regularization of data.

Keywords : Wave equation Regularization of data Regularization of problems Distributions Nonlinear generalized functions Nonlinear problems Characteristic problems

Document type :

Journal articles

Domain :

Mathematics [math] / Functional Analysis [math.FA]

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https://hal.univ-antilles.fr/hal-01529550
Contributor : Antoine Delcroix <>
Submitted on : Wednesday, May 31, 2017 - 4:12:12 AM
Last modification on : Friday, May 21, 2021 - 1:46:06 PM

Generalized solutions of singular differential problems. Relationship with classical solutions

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Generalized solutions of singular differential problems. Relationship with classical solutions

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