Generalized solutions of singular differential problems. Relationship with classical solutions

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.
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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 : Tuesday, December 18, 2018 - 10:56:29 AM

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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. ⟨https://www.journals.elsevier.com/journal-of-mathematical-analysis-and-applications⟩. ⟨10.1016/j.jmaa.2008.11.077⟩. ⟨hal-01529550⟩

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