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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
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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

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Antoine Delcroix, Victor Devoue, Jean-André Marti. Generalized solutions of singular differential problems. Relationship with classical solutions. Journal of Mathematical Analysis and Applications, Elsevier, 2008, 353, pp.386-402. ⟨10.1016/j.jmaa.2008.11.077⟩. ⟨hal-01529550⟩

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